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Theorem 2vwomr1a 363
Description: 2-variable WOML rule.
Hypothesis
Ref Expression
2vwomr1a.1 (a ->1 b) = 1
Assertion
Ref Expression
2vwomr1a (a ->2 b) = 1
Proof of Theorem 2vwomr1a
StepHypRef Expression
1 df-i2 45 . 2 (a ->2 b) = (b v (a' ^ b'))
2 df-i1 44 . . . . 5 (a ->1 b) = (a' v (a ^ b))
32ax-r1 35 . . . 4 (a' v (a ^ b)) = (a ->1 b)
4 2vwomr1a.1 . . . 4 (a ->1 b) = 1
53, 4ax-r2 36 . . 3 (a' v (a ^ b)) = 1
65ax-wom 361 . 2 (b v (a' ^ b')) = 1
71, 6ax-r2 36 1 (a ->2 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-r1 35  ax-r2 36  ax-wom 361
This theorem depends on definitions:  df-i1 44  df-i2 45
This theorem is referenced by:  wr5-2v  366  lem3.4.3  1076  lem3.4.5  1078
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