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Theorem wql2lem3 290
Description: Lemma for ->2 WQL axiom.
Hypothesis
Ref Expression
wql2lem3.1 (a ->2 b) = 1
Assertion
Ref Expression
wql2lem3 ((a ^ b') ->2 a') = 1
Proof of Theorem wql2lem3
StepHypRef Expression
1 df-i2 45 . 2 ((a ^ b') ->2 a') = (a' v ((a ^ b')' ^ a''))
2 oran2 92 . . . . . 6 (a' v b) = (a ^ b')'
32ax-r1 35 . . . . 5 (a ^ b')' = (a' v b)
43ran 78 . . . 4 ((a ^ b')' ^ a'') = ((a' v b) ^ a'')
5 ancom 74 . . . 4 ((a' v b) ^ a'') = (a'' ^ (a' v b))
64, 5ax-r2 36 . . 3 ((a ^ b')' ^ a'') = (a'' ^ (a' v b))
76lor 70 . 2 (a' v ((a ^ b')' ^ a'')) = (a' v (a'' ^ (a' v b)))
8 wql2lem3.1 . . . 4 (a ->2 b) = 1
98wql2lem 288 . . 3 (a' v b) = 1
10 omlem2 128 . . 3 ((a' v b)' v (a' v (a'' ^ (a' v b)))) = 1
119, 10skr0 242 . 2 (a' v (a'' ^ (a' v b))) = 1
121, 7, 113tr 65 1 ((a ^ b') ->2 a') = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i2 45  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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