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Theorem u1lemonb 635
Description: Lemma for Sasaki implication study.
Assertion
Ref Expression
u1lemonb ((a ->1 b) v b') = 1
Proof of Theorem u1lemonb
StepHypRef Expression
1 df-i1 44 . . 3 (a ->1 b) = (a' v (a ^ b))
21ax-r5 38 . 2 ((a ->1 b) v b') = ((a' v (a ^ b)) v b')
3 or32 82 . . 3 ((a' v (a ^ b)) v b') = ((a' v b') v (a ^ b))
4 df-a 40 . . . . 5 (a ^ b) = (a' v b')'
54lor 70 . . . 4 ((a' v b') v (a ^ b)) = ((a' v b') v (a' v b')')
6 df-t 41 . . . . 5 1 = ((a' v b') v (a' v b')')
76ax-r1 35 . . . 4 ((a' v b') v (a' v b')') = 1
85, 7ax-r2 36 . . 3 ((a' v b') v (a ^ b)) = 1
93, 8ax-r2 36 . 2 ((a' v (a ^ b)) v b') = 1
102, 9ax-r2 36 1 ((a ->1 b) v b') = 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-r1 35  ax-r2 36  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-i1 44
This theorem is referenced by:  u1lemnab  650  u3lem14a  791
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