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Theorem ud3lem3c 574
Description: Lemma for unified disjunction.
Assertion
Ref Expression
ud3lem3c ((a ->3 b)' v (a v b)) = (a v b)
Proof of Theorem ud3lem3c
StepHypRef Expression
1 ud3lem0c 279 . . . 4 (a ->3 b)' = (((a v b') ^ (a v b)) ^ (a' v (a ^ b')))
2 an32 83 . . . . 5 (((a v b') ^ (a v b)) ^ (a' v (a ^ b'))) = (((a v b') ^ (a' v (a ^ b'))) ^ (a v b))
3 ancom 74 . . . . 5 (((a v b') ^ (a' v (a ^ b'))) ^ (a v b)) = ((a v b) ^ ((a v b') ^ (a' v (a ^ b'))))
42, 3ax-r2 36 . . . 4 (((a v b') ^ (a v b)) ^ (a' v (a ^ b'))) = ((a v b) ^ ((a v b') ^ (a' v (a ^ b'))))
51, 4ax-r2 36 . . 3 (a ->3 b)' = ((a v b) ^ ((a v b') ^ (a' v (a ^ b'))))
65ax-r5 38 . 2 ((a ->3 b)' v (a v b)) = (((a v b) ^ ((a v b') ^ (a' v (a ^ b')))) v (a v b))
7 ax-a2 31 . . 3 (((a v b) ^ ((a v b') ^ (a' v (a ^ b')))) v (a v b)) = ((a v b) v ((a v b) ^ ((a v b') ^ (a' v (a ^ b')))))
8 orabs 120 . . 3 ((a v b) v ((a v b) ^ ((a v b') ^ (a' v (a ^ b'))))) = (a v b)
97, 8ax-r2 36 . 2 (((a v b) ^ ((a v b') ^ (a' v (a ^ b')))) v (a v b)) = (a v b)
106, 9ax-r2 36 1 ((a ->3 b)' v (a v b)) = (a v b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->3 wi3 14
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-a 40  df-i3 46
This theorem is referenced by:  ud3lem3d  575
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