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Theorem womle3b 297
Description: Implied by the WOM law. (Contributed by NM, 27-Jan-1999.)
Hypothesis
Ref Expression
womle3b.1 ((a1 b) ∪ (a2 b)) = 1
Assertion
Ref Expression
womle3b (a ∩ (a1 b)) ≤ ((a1 b) ∪ (a2 b))

Proof of Theorem womle3b
StepHypRef Expression
1 le1 146 . 2 (a ∩ (a1 b)) ≤ 1
2 womle3b.1 . . 3 ((a1 b) ∪ (a2 b)) = 1
32ax-r1 35 . 2 1 = ((a1 b) ∪ (a2 b))
41, 3lbtr 139 1 (a ∩ (a1 b)) ≤ ((a1 b) ∪ (a2 b))
Colors of variables: term
Syntax hints:   = wb 1  wle 2   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-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-le1 130  df-le2 131
This theorem is referenced by: (None)
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