Theorem womle3b 297

Description: Implied by the WOM law. (Contributed by NM, 27-Jan-1999.)

Hypothesis

Ref	Expression
womle3b.1	((a →1 b)⊥ ∪ (a →2 b)) = 1

Assertion

Ref	Expression
womle3b	(a ∩ (a →1 b)) ≤ ((a →1 b)⊥ ∪ (a →2 b))

Proof of Theorem womle3b

Step	Hyp	Ref	Expression
1		le1 146	. 2 (a ∩ (a →1 b)) ≤ 1
2		womle3b.1	. . 3 ((a →1 b)⊥ ∪ (a →2 b)) = 1
3	2	ax-r1 35	. 2 1 = ((a →1 b)⊥ ∪ (a →2 b))
4	1, 3	lbtr 139	1 (a ∩ (a →1 b)) ≤ ((a →1 b)⊥ ∪ (a →2 b))

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)