:: PROCAL_1 semantic presentation
theorem Th1: :: PROCAL_1:1
Lemma10:
for p, q being Element of CQC-WFF holds p 'or' q = ('not' p) => q
theorem Th2: :: PROCAL_1:2
theorem Th3: :: PROCAL_1:3
theorem Th4: :: PROCAL_1:4
theorem Th5: :: PROCAL_1:5
theorem Th6: :: PROCAL_1:6
theorem Th7: :: PROCAL_1:7
theorem Th8: :: PROCAL_1:8
theorem Th9: :: PROCAL_1:9
theorem Th10: :: PROCAL_1:10
theorem Th11: :: PROCAL_1:11
theorem Th12: :: PROCAL_1:12
theorem Th13: :: PROCAL_1:13
theorem Th14: :: PROCAL_1:14
Lemma21:
for p, q being Element of CQC-WFF holds (p '&' q) => (('not' ('not' p)) '&' q) in TAUT
Lemma22:
for p, q being Element of CQC-WFF holds (('not' ('not' p)) '&' q) => (p '&' q) in TAUT
theorem Th15: :: PROCAL_1:15
theorem Th16: :: PROCAL_1:16
theorem Th17: :: PROCAL_1:17
theorem Th18: :: PROCAL_1:18
theorem Th19: :: PROCAL_1:19
theorem Th20: :: PROCAL_1:20
theorem Th21: :: PROCAL_1:21
theorem Th22: :: PROCAL_1:22
theorem Th23: :: PROCAL_1:23
theorem Th24: :: PROCAL_1:24
theorem Th25: :: PROCAL_1:25
theorem Th26: :: PROCAL_1:26
theorem Th27: :: PROCAL_1:27
theorem Th28: :: PROCAL_1:28
theorem Th29: :: PROCAL_1:29
Lemma41:
for p, q being Element of CQC-WFF st p in TAUT & q in TAUT holds
p '&' q in TAUT
theorem Th30: :: PROCAL_1:30
theorem Th31: :: PROCAL_1:31
theorem Th32: :: PROCAL_1:32
theorem Th33: :: PROCAL_1:33
theorem Th34: :: PROCAL_1:34
theorem Th35: :: PROCAL_1:35
theorem Th36: :: PROCAL_1:36
theorem Th37: :: PROCAL_1:37
theorem Th38: :: PROCAL_1:38
theorem Th39: :: PROCAL_1:39
theorem Th40: :: PROCAL_1:40
Lemma55:
for p, q, r being Element of CQC-WFF st p => q in TAUT holds
(r '&' p) => (r '&' q) in TAUT
Lemma56:
for p, q, r being Element of CQC-WFF st p => q in TAUT holds
(p 'or' r) => (q 'or' r) in TAUT
Lemma57:
for p, q, r being Element of CQC-WFF st p => q in TAUT holds
(r 'or' p) => (r 'or' q) in TAUT
theorem Th41: :: PROCAL_1:41
theorem Th42: :: PROCAL_1:42
theorem Th43: :: PROCAL_1:43
theorem Th44: :: PROCAL_1:44
theorem Th45: :: PROCAL_1:45
theorem Th46: :: PROCAL_1:46
theorem Th47: :: PROCAL_1:47
theorem Th48: :: PROCAL_1:48
theorem Th49: :: PROCAL_1:49
theorem Th50: :: PROCAL_1:50
theorem Th51: :: PROCAL_1:51
theorem Th52: :: PROCAL_1:52
theorem Th53: :: PROCAL_1:53
theorem Th54: :: PROCAL_1:54
theorem Th55: :: PROCAL_1:55
theorem Th56: :: PROCAL_1:56
theorem Th57: :: PROCAL_1:57
theorem Th58: :: PROCAL_1:58