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Theorem omlem1 127
Description: Lemma in proof of Th. 1 of Pavicic 1987.
Assertion
Ref Expression
omlem1 ((a v (a' ^ (a v b))) v (a v b)) = (a v b)
Proof of Theorem omlem1
StepHypRef Expression
1 ax-a2 31 . . 3 ((a v (a' ^ (a v b))) v (a v b)) = ((a v b) v (a v (a' ^ (a v b))))
2 ax-a3 32 . . 3 (((a v (a' ^ (a v b))) v a) v b) = ((a v (a' ^ (a v b))) v (a v b))
3 ax-a3 32 . . 3 (((a v b) v a) v (a' ^ (a v b))) = ((a v b) v (a v (a' ^ (a v b))))
41, 2, 33tr1 63 . 2 (((a v (a' ^ (a v b))) v a) v b) = (((a v b) v a) v (a' ^ (a v b)))
5 ax-a3 32 . . . . . . 7 ((a v a) v b) = (a v (a v b))
6 ax-a2 31 . . . . . . 7 (a v (a v b)) = ((a v b) v a)
75, 6ax-r2 36 . . . . . 6 ((a v a) v b) = ((a v b) v a)
87ax-r1 35 . . . . 5 ((a v b) v a) = ((a v a) v b)
9 oridm 110 . . . . . 6 (a v a) = a
109ax-r5 38 . . . . 5 ((a v a) v b) = (a v b)
118, 10ax-r2 36 . . . 4 ((a v b) v a) = (a v b)
12 ancom 74 . . . 4 (a' ^ (a v b)) = ((a v b) ^ a')
1311, 122or 72 . . 3 (((a v b) v a) v (a' ^ (a v b))) = ((a v b) v ((a v b) ^ a'))
14 orabs 120 . . 3 ((a v b) v ((a v b) ^ a')) = (a v b)
1513, 14ax-r2 36 . 2 (((a v b) v a) v (a' ^ (a v b))) = (a v b)
164, 2, 153tr2 64 1 ((a v (a' ^ (a v b))) v (a v b)) = (a v b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7
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-t 41  df-f 42
This theorem is referenced by:  woml  211  oml  445
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