Theorem wlor 350

Description: Weak orthomodular law.

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 30	. . 3 (c ∪ a) = (a ∪ c)
2		ax-a2 30	. . 3 (c ∪ b) = (b ∪ c)
3	1, 2	2bi 91	. 2 ((c ∪ a) ≡ (c ∪ b)) = ((a ∪ c) ≡ (b ∪ c))
4		wlor.1	. . 3 (a ≡ b) = 1
5	4	wr5-2v 348	. 2 ((a ∪ c) ≡ (b ∪ c)) = 1
6	3, 5	ax-r2 35	1 ((c ∪ a) ≡ (c ∪ b)) = 1

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

This theorem is referenced by:  wr2 353  w2or 354  wleao 359  wom4 362  wom5 363  wcomlem 364  wcom3i 404  wfh3 407  wfh4 408  wlem14 412  ska2 414  ska4 415

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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