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Theorem u1lemona 625
Description: Lemma for Sasaki implication study.
Assertion
Ref Expression
u1lemona ((a ->1 b) v a') = (a' v (a ^ b))
Proof of Theorem u1lemona
StepHypRef Expression
1 df-i1 44 . . 3 (a ->1 b) = (a' v (a ^ b))
21ax-r5 38 . 2 ((a ->1 b) v a') = ((a' v (a ^ b)) v a')
3 or32 82 . . 3 ((a' v (a ^ b)) v a') = ((a' v a') v (a ^ b))
4 oridm 110 . . . 4 (a' v a') = a'
54ax-r5 38 . . 3 ((a' v a') v (a ^ b)) = (a' v (a ^ b))
63, 5ax-r2 36 . 2 ((a' v (a ^ b)) v a') = (a' v (a ^ b))
72, 6ax-r2 36 1 ((a ->1 b) v a') = (a' v (a ^ b))
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-t 41  df-f 42  df-i1 44
This theorem is referenced by:  u1lemnaa  640  u1lem4  757
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