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Theorem 2vwomr2a 364
Description: 2-variable WOML rule.
Hypothesis
Ref Expression
2vwomr2a.1 (a ->2 b) = 1
Assertion
Ref Expression
2vwomr2a (a ->1 b) = 1
Proof of Theorem 2vwomr2a
StepHypRef Expression
1 df-i1 44 . 2 (a ->1 b) = (a' v (a ^ b))
2 df-i2 45 . . . . 5 (a ->2 b) = (b v (a' ^ b'))
32ax-r1 35 . . . 4 (b v (a' ^ b')) = (a ->2 b)
4 2vwomr2a.1 . . . 4 (a ->2 b) = 1
53, 4ax-r2 36 . . 3 (b v (a' ^ b')) = 1
652vwomr2 362 . 2 (a' v (a ^ b)) = 1
71, 6ax-r2 36 1 (a ->1 b) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->1 wi1 12   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361
This theorem depends on definitions:  df-a 40  df-i1 44  df-i2 45
This theorem is referenced by:  lem3.4.3  1076
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