Theorem wom3 349

Description: Weak orthomodular law for study of weakly orthomodular lattices.

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 138	. 2 a ≤ 1
2		wom3.1	. . . . 5 (a ≡ b) = 1
3	2	wr5-2v 348	. . . 4 ((a ∪ c) ≡ (b ∪ c)) = 1
4	3	ax-r1 34	. . 3 1 = ((a ∪ c) ≡ (b ∪ c))
5	4	bile 134	. 2 1 ≤ ((a ∪ c) ≡ (b ∪ c))
6	1, 5	letr 129	1 a ≤ ((a ∪ c) ≡ (b ∪ c))

Syntax hints:   = wb 1   ≤ wle 2   ≡ tb 5   ∪ wo 6  1wt 9

This theorem is referenced by:  wr5 413

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-wom 343

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44  df-le1 122  df-le2 123

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