Theorem r3a 440

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 41	. . 3 1 = (a v a')
3		df-b 39	. . 3 (a == b) = ((a' v b')' v (a v b)')
4	1, 2, 3	3tr2 64	. 2 (a v a') = ((a' v b')' v (a v b)')
5	4	ax-r3 439	1 a = b

Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6  1wt 8

This theorem is referenced by:  wed 441  lem3.1 443  oi3oa3lem1 732  oi3oa3 733

This theorem was proved from axioms:  ax-r1 35  ax-r2 36  ax-r3 439

This theorem depends on definitions:  df-b 39  df-t 41

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