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Theorem 2vwomr2 362
 Description: 2-variable WOML rule. (Contributed by NM, 13-Nov-1998.)
Hypothesis
Ref Expression
2vwomr2.1 (b ∪ (ab )) = 1
Assertion
Ref Expression
2vwomr2 (a ∪ (ab)) = 1

Proof of Theorem 2vwomr2
StepHypRef Expression
1 ancom 74 . . . 4 (ab) = (ba)
2 ax-a1 30 . . . . 5 b = b
3 ax-a1 30 . . . . 5 a = a
42, 32an 79 . . . 4 (ba) = (b a )
51, 4ax-r2 36 . . 3 (ab) = (b a )
65lor 70 . 2 (a ∪ (ab)) = (a ∪ (b a ))
7 ancom 74 . . . . . 6 (ab ) = (ba )
82, 72or 72 . . . . 5 (b ∪ (ab )) = (b ∪ (ba ))
98ax-r1 35 . . . 4 (b ∪ (ba )) = (b ∪ (ab ))
10 2vwomr2.1 . . . 4 (b ∪ (ab )) = 1
119, 10ax-r2 36 . . 3 (b ∪ (ba )) = 1
1211ax-wom 361 . 2 (a ∪ (b a )) = 1
136, 12ax-r2 36 1 (a ∪ (ab)) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8 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 This theorem is referenced by:  2vwomr2a  364  2vwomlem  365
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