Theorem r3a 422

Description: Orthomodular law restated.

Hypothesis

Ref	Expression
r3a.1	1 = (a == b)

Assertion

Ref	Expression
r3a	a = b

Proof of Theorem r3a

Step	Hyp	Ref	Expression
1		r3a.1	. . 3 1 = (a == b)
2		df-t 40	. . 3 1 = (a v a_|_)
3		df-b 38	. . 3 (a == b) = ((a_|_ v b_|_)_|_ v (a v b)_|_)
4	1, 2, 3	3tr2 61	. 2 (a v a_|_) = ((a_|_ v b_|_)_|_ v (a v b)_|_)
5	4	ax-r3 421	1 a = b

Syntax hints:   = wb 1  _|_wn 4   == tb 5   v wo 6  1wt 9

This theorem is referenced by:  wed 423  lem3.1 425  oi3oa3lem1 714  oi3oa3 715

This theorem was proved from axioms:  ax-r1 34  ax-r2 35  ax-r3 421

This theorem depends on definitions:  df-b 38  df-t 40

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