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Theorem u1lemana 605
Description: Lemma for Sasaki implication study.
Assertion
Ref Expression
u1lemana ((a ->1 b) ^ a') = a'
Proof of Theorem u1lemana
StepHypRef Expression
1 df-i1 44 . . 3 (a ->1 b) = (a' v (a ^ b))
21ran 78 . 2 ((a ->1 b) ^ a') = ((a' v (a ^ b)) ^ a')
3 ancom 74 . . 3 ((a' v (a ^ b)) ^ a') = (a' ^ (a' v (a ^ b)))
4 anabs 121 . . 3 (a' ^ (a' v (a ^ b))) = a'
53, 4ax-r2 36 . 2 ((a' v (a ^ b)) ^ a') = a'
62, 5ax-r2 36 1 ((a ->1 b) ^ a') = a'
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-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i1 44
This theorem is referenced by:  u1lemnoa  660  u12lembi  726  u1lem7  772
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