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Theorem womle 298
 Description: An equality implying the WOM law.
Hypothesis
Ref Expression
womle.1 (a ∩ (a1 b)) = (a ∩ (a2 b))
Assertion
Ref Expression
womle ((a2 b) ∪ (a1 b)) = 1

Proof of Theorem womle
StepHypRef Expression
1 womle.1 . . . . 5 (a ∩ (a1 b)) = (a ∩ (a2 b))
21ax-r1 35 . . . 4 (a ∩ (a2 b)) = (a ∩ (a1 b))
3 lear 161 . . . 4 (a ∩ (a1 b)) ≤ (a1 b)
42, 3bltr 138 . . 3 (a ∩ (a2 b)) ≤ (a1 b)
5 leor 159 . . 3 (a1 b) ≤ ((a2 b) ∪ (a1 b))
64, 5letr 137 . 2 (a ∩ (a2 b)) ≤ ((a2 b) ∪ (a1 b))
76womle2a 295 1 ((a2 b) ∪ (a1 b)) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ 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-a3 32  ax-a4 33  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  df-i1 44  df-le1 130  df-le2 131 This theorem is referenced by: (None)
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