Theorem r3b 424

Description: Orthomodular law from weak equivalential detachment (WBMP).

Hypothesis

Ref	Expression
r3b.1	(c ∪ c⊥ ) = (a ≡ b)

Assertion

Ref	Expression
r3b	a = b

Proof of Theorem r3b

Step	Hyp	Ref	Expression
1		df-t 40	. . 3 1 = (c ∪ c⊥ )
2		r3b.1	. . 3 (c ∪ c⊥ ) = (a ≡ b)
3	1, 2	ax-r2 35	. 2 1 = (a ≡ b)
4		1b 109	. 2 (1 ≡ (a ≡ b)) = (a ≡ b)
5	3, 4	wed 423	1 a = b

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5   ∪ wo 6  1wt 9

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41

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