Theorem womle2b 288

Description: An equivalent to the WOM law.

Hypothesis

Ref	Expression
womle2b.1	((a →2 b)⊥ ∪ (a →1 b)) = 1

Assertion

Ref	Expression
womle2b	(a ∩ (a →2 b)) ≤ ((a →2 b)⊥ ∪ (a →1 b))

Proof of Theorem womle2b

Step	Hyp	Ref	Expression
1		le1 138	. 2 (a ∩ (a →2 b)) ≤ 1
2		womle2b.1	. . 3 ((a →2 b)⊥ ∪ (a →1 b)) = 1
3	2	ax-r1 34	. 2 1 = ((a →2 b)⊥ ∪ (a →1 b))
4	1, 3	lbtr 131	1 (a ∩ (a →2 b)) ≤ ((a →2 b)⊥ ∪ (a →1 b))

Syntax hints:   = wb 1   ≤ wle 2  ^⊥ wn 4   ∪ 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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