Theorem womle3b 289

Description: Implied by the WOM law.

Hypothesis

Ref	Expression
womle3b.1	((a ->1 b)_|_ v (a ->2 b)) = 1

Assertion

Ref	Expression
womle3b	(a ^ (a ->1 b)) =< ((a ->1 b)_|_ v (a ->2 b))

Proof of Theorem womle3b

Step	Hyp	Ref	Expression
1		le1 138	. 2 (a ^ (a ->1 b)) =< 1
2		womle3b.1	. . 3 ((a ->1 b)_|_ v (a ->2 b)) = 1
3	2	ax-r1 34	. 2 1 = ((a ->1 b)_|_ v (a ->2 b))
4	1, 3	lbtr 131	1 (a ^ (a ->1 b)) =< ((a ->1 b)_|_ v (a ->2 b))

Syntax hints:   = wb 1   =< wle 2  _|_wn 4   v wo 6   ^ wa 7  1wt 9   ->1 wi1 13   ->2 wi2 14

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-t 40  df-le1 122  df-le2 123

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