:: CQC_THE2 semantic presentation
theorem Th1: :: CQC_THE2:1
theorem Th2: :: CQC_THE2:2
theorem Th3: :: CQC_THE2:3
theorem Th4: :: CQC_THE2:4
Lemma41:
for p, q being Element of CQC-WFF holds
( (p '&' q) => p is valid & (p '&' q) => q is valid )
Lemma42:
for p, q being Element of CQC-WFF st p '&' q is valid holds
( p is valid & q is valid )
Lemma43:
for p, q, r being Element of CQC-WFF st p => q is valid & p => r is valid holds
p => (q '&' r) is valid
Lemma44:
for p, q, r, t being Element of CQC-WFF st p => q is valid & r => t is valid holds
(p 'or' r) => (q 'or' t) is valid
Lemma45:
for p, q, r, t being Element of CQC-WFF st p => q is valid & r => t is valid holds
(p '&' r) => (q '&' t) is valid
Lemma46:
for p, q being Element of CQC-WFF holds
( p => (p 'or' q) is valid & p => (q 'or' p) is valid )
Lemma47:
for p, q, r being Element of CQC-WFF st p => q is valid & r => q is valid holds
(p 'or' r) => q is valid
Lemma48:
for p, q being Element of CQC-WFF st p is valid & q is valid holds
p '&' q is valid
Lemma49:
for p, q, r being Element of CQC-WFF st p => q is valid holds
(r '&' p) => (r '&' q) is valid
Lemma50:
for p, q, r being Element of CQC-WFF st p => q is valid holds
(p 'or' r) => (q 'or' r) is valid
Lemma51:
for p, q being Element of CQC-WFF holds (p 'or' q) => (('not' p) => q) is valid
Lemma52:
for p, q being Element of CQC-WFF holds (('not' p) => q) => (p 'or' q) is valid
Lemma53:
for p being Element of CQC-WFF holds p <=> p is valid
Lemma54:
for p, q being Element of CQC-WFF holds
( ( p => q is valid & q => p is valid ) iff p <=> q is valid )
Lemma55:
for p, q being Element of CQC-WFF st p <=> q is valid holds
( p is valid iff q is valid )
Lemma57:
for p, q, r, t being Element of CQC-WFF st p => (q => r) is valid & r => t is valid holds
p => (q => t) is valid
theorem Th5: :: CQC_THE2:5
theorem Th6: :: CQC_THE2:6
theorem Th7: :: CQC_THE2:7
theorem Th8: :: CQC_THE2:8
canceled;
theorem Th9: :: CQC_THE2:9
theorem Th10: :: CQC_THE2:10
theorem Th11: :: CQC_THE2:11
theorem Th12: :: CQC_THE2:12
theorem Th13: :: CQC_THE2:13
canceled;
theorem Th14: :: CQC_THE2:14
theorem Th15: :: CQC_THE2:15
theorem Th16: :: CQC_THE2:16
canceled;
theorem Th17: :: CQC_THE2:17
theorem Th18: :: CQC_THE2:18
theorem Th19: :: CQC_THE2:19
theorem Th20: :: CQC_THE2:20
theorem Th21: :: CQC_THE2:21
theorem Th22: :: CQC_THE2:22
theorem Th23: :: CQC_THE2:23
theorem Th24: :: CQC_THE2:24
theorem Th25: :: CQC_THE2:25
theorem Th26: :: CQC_THE2:26
theorem Th27: :: CQC_THE2:27
theorem Th28: :: CQC_THE2:28
theorem Th29: :: CQC_THE2:29
theorem Th30: :: CQC_THE2:30
theorem Th31: :: CQC_THE2:31
theorem Th32: :: CQC_THE2:32
theorem Th33: :: CQC_THE2:33
canceled;
theorem Th34: :: CQC_THE2:34
theorem Th35: :: CQC_THE2:35
theorem Th36: :: CQC_THE2:36
theorem Th37: :: CQC_THE2:37
theorem Th38: :: CQC_THE2:38
theorem Th39: :: CQC_THE2:39
theorem Th40: :: CQC_THE2:40
theorem Th41: :: CQC_THE2:41
theorem Th42: :: CQC_THE2:42
theorem Th43: :: CQC_THE2:43
theorem Th44: :: CQC_THE2:44
theorem Th45: :: CQC_THE2:45
theorem Th46: :: CQC_THE2:46
theorem Th47: :: CQC_THE2:47
theorem Th48: :: CQC_THE2:48
theorem Th49: :: CQC_THE2:49
theorem Th50: :: CQC_THE2:50
theorem Th51: :: CQC_THE2:51
theorem Th52: :: CQC_THE2:52
theorem Th53: :: CQC_THE2:53
theorem Th54: :: CQC_THE2:54
theorem Th55: :: CQC_THE2:55
theorem Th56: :: CQC_THE2:56
theorem Th57: :: CQC_THE2:57
theorem Th58: :: CQC_THE2:58
theorem Th59: :: CQC_THE2:59
theorem Th60: :: CQC_THE2:60
theorem Th61: :: CQC_THE2:61
theorem Th62: :: CQC_THE2:62
theorem Th63: :: CQC_THE2:63
theorem Th64: :: CQC_THE2:64
theorem Th65: :: CQC_THE2:65
theorem Th66: :: CQC_THE2:66
theorem Th67: :: CQC_THE2:67
theorem Th68: :: CQC_THE2:68
theorem Th69: :: CQC_THE2:69
theorem Th70: :: CQC_THE2:70
theorem Th71: :: CQC_THE2:71
theorem Th72: :: CQC_THE2:72
theorem Th73: :: CQC_THE2:73
theorem Th74: :: CQC_THE2:74
theorem Th75: :: CQC_THE2:75
theorem Th76: :: CQC_THE2:76
theorem Th77: :: CQC_THE2:77
Lemma99:
for p, q being Element of CQC-WFF
for x being bound_QC-variable st not x in still_not-bound_in p holds
(All x,(p => q)) => (p => (All x,q)) is valid
theorem Th78: :: CQC_THE2:78
theorem Th79: :: CQC_THE2:79
theorem Th80: :: CQC_THE2:80
theorem Th81: :: CQC_THE2:81
theorem Th82: :: CQC_THE2:82
theorem Th83: :: CQC_THE2:83
theorem Th84: :: CQC_THE2:84
theorem Th85: :: CQC_THE2:85
theorem Th86: :: CQC_THE2:86
theorem Th87: :: CQC_THE2:87
theorem Th88: :: CQC_THE2:88
theorem Th89: :: CQC_THE2:89
theorem Th90: :: CQC_THE2:90
theorem Th91: :: CQC_THE2:91
theorem Th92: :: CQC_THE2:92
theorem Th93: :: CQC_THE2:93
theorem Th94: :: CQC_THE2:94
theorem Th95: :: CQC_THE2:95
theorem Th96: :: CQC_THE2:96