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Theorem omlem2 128
Description: Lemma in proof of Th. 1 of Pavicic 1987.
Assertion
Ref Expression
omlem2 ((a v b)' v (a v (a' ^ (a v b)))) = 1
Proof of Theorem omlem2
StepHypRef Expression
1 ax-a2 31 . . 3 ((a v b)' v a) = (a v (a v b)')
2 anor2 89 . . 3 (a' ^ (a v b)) = (a v (a v b)')'
31, 22or 72 . 2 (((a v b)' v a) v (a' ^ (a v b))) = ((a v (a v b)') v (a v (a v b)')')
4 ax-a3 32 . . 3 (((a v b)' v a) v (a' ^ (a v b))) = ((a v b)' v (a v (a' ^ (a v b))))
54ax-r1 35 . 2 ((a v b)' v (a v (a' ^ (a v b)))) = (((a v b)' v a) v (a' ^ (a v b)))
6 df-t 41 . 2 1 = ((a v (a v b)') v (a v (a v b)')')
73, 5, 63tr1 63 1 ((a v b)' v (a v (a' ^ (a v b)))) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41
This theorem is referenced by:  woml  211  wql2lem3  290  oml  445
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