Theorem wr5 431

Description: Proof of weak orthomodular law from weaker-looking equivalent, wom3 367, which in turn is derived from ax-wom 361. (Contributed by NM, 25-Oct-1997.)

Hypothesis

Ref	Expression
wr5.1	(a ≡ b) = 1

Assertion

Ref	Expression
wr5	((a ∪ c) ≡ (b ∪ c)) = 1

Proof of Theorem wr5

Step	Hyp	Ref	Expression
1		wr5.1	. 2 (a ≡ b) = 1
2	1	wr5-2v 366	1 ((a ∪ c) ≡ (b ∪ c)) = 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:  wdka4o  1116