Theorem wom3 367

Description: Weak orthomodular law for study of weakly orthomodular lattices. (Contributed by NM, 13-Nov-1998.)

Hypothesis

Ref	Expression
wom3.1	(a ≡ b) = 1

Assertion

Ref	Expression
wom3	a ≤ ((a ∪ c) ≡ (b ∪ c))

Proof of Theorem wom3

Step	Hyp	Ref	Expression
1		le1 146	. 2 a ≤ 1
2		wom3.1	. . . . 5 (a ≡ b) = 1
3	2	wr5-2v 366	. . . 4 ((a ∪ c) ≡ (b ∪ c)) = 1
4	3	ax-r1 35	. . 3 1 = ((a ∪ c) ≡ (b ∪ c))
5	4	bile 142	. 2 1 ≤ ((a ∪ c) ≡ (b ∪ c))
6	1, 5	letr 137	1 a ≤ ((a ∪ c) ≡ (b ∪ c))

Syntax hints:   = wb 1   ≤ wle 2   ≡ tb 5   ∪ wo 6  1wt 8

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  ax-wom 361

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le1 130  df-le2 131

This theorem is referenced by: (None)