Theorem wlor 368

Description: Weak orthomodular law. (Contributed by NM, 24-Sep-1997.)

Hypothesis

Ref	Expression
wlor.1	(a ≡ b) = 1

Assertion

Ref	Expression
wlor	((c ∪ a) ≡ (c ∪ b)) = 1

Proof of Theorem wlor

Step	Hyp	Ref	Expression
1		ax-a2 31	. . 3 (c ∪ a) = (a ∪ c)
2		ax-a2 31	. . 3 (c ∪ b) = (b ∪ c)
3	1, 2	2bi 99	. 2 ((c ∪ a) ≡ (c ∪ b)) = ((a ∪ c) ≡ (b ∪ c))
4		wlor.1	. . 3 (a ≡ b) = 1
5	4	wr5-2v 366	. 2 ((a ∪ c) ≡ (b ∪ c)) = 1
6	3, 5	ax-r2 36	1 ((c ∪ a) ≡ (c ∪ b)) = 1

Syntax hints:   = wb 1   ≡ 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:  wr2  371  w2or  372  wleao  377  wom4  380  wom5  381  wcomlem  382  wcom3i  422  wfh3  425  wfh4  426  wlem14  430  ska2  432  ska4  433