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Theorem u2lemona 626
Description: Lemma for Dishkant implication study.
Assertion
Ref Expression
u2lemona ((a ->2 b) v a') = (a' v b)
Proof of Theorem u2lemona
StepHypRef Expression
1 df-i2 45 . . 3 (a ->2 b) = (b v (a' ^ b'))
21ax-r5 38 . 2 ((a ->2 b) v a') = ((b v (a' ^ b')) v a')
3 ax-a3 32 . . 3 ((b v (a' ^ b')) v a') = (b v ((a' ^ b') v a'))
4 ax-a2 31 . . . 4 (b v ((a' ^ b') v a')) = (((a' ^ b') v a') v b)
5 lea 160 . . . . . 6 (a' ^ b') =< a'
65df-le2 131 . . . . 5 ((a' ^ b') v a') = a'
76ax-r5 38 . . . 4 (((a' ^ b') v a') v b) = (a' v b)
84, 7ax-r2 36 . . 3 (b v ((a' ^ b') v a')) = (a' v b)
93, 8ax-r2 36 . 2 ((b v (a' ^ b')) v a') = (a' v b)
102, 9ax-r2 36 1 ((a ->2 b) v a') = (a' v b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->2 wi2 13
This theorem was proved from axioms:  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i2 45  df-le1 130  df-le2 131
This theorem is referenced by:  u2lemnaa  641
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