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Theorem u1lemoa 620
Description: Lemma for Sasaki implication study.
Assertion
Ref Expression
u1lemoa ((a ->1 b) v a) = 1
Proof of Theorem u1lemoa
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 ax-a2 31 . . 3 ((a' v (a ^ b)) v a) = (a v (a' v (a ^ b)))
4 ax-a3 32 . . . . 5 ((a v a') v (a ^ b)) = (a v (a' v (a ^ b)))
54ax-r1 35 . . . 4 (a v (a' v (a ^ b))) = ((a v a') v (a ^ b))
6 ax-a2 31 . . . . 5 ((a v a') v (a ^ b)) = ((a ^ b) v (a v a'))
7 df-t 41 . . . . . . . 8 1 = (a v a')
87lor 70 . . . . . . 7 ((a ^ b) v 1) = ((a ^ b) v (a v a'))
98ax-r1 35 . . . . . 6 ((a ^ b) v (a v a')) = ((a ^ b) v 1)
10 or1 104 . . . . . 6 ((a ^ b) v 1) = 1
119, 10ax-r2 36 . . . . 5 ((a ^ b) v (a v a')) = 1
126, 11ax-r2 36 . . . 4 ((a v a') v (a ^ b)) = 1
135, 12ax-r2 36 . . 3 (a v (a' v (a ^ b))) = 1
143, 13ax-r2 36 . 2 ((a' v (a ^ b)) v a) = 1
152, 14ax-r2 36 1 ((a ->1 b) v a) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->1 wi1 12
This theorem was proved from axioms:  ax-a2 31  ax-a3 32  ax-a4 33  ax-r1 35  ax-r2 36  ax-r5 38
This theorem depends on definitions:  df-t 41  df-i1 44
This theorem is referenced by:  u1lemnana  645  oi3oa3lem1  732  i1orni1  847  oau  929
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