Theorem u2lemnonb 658

Description: Lemma for Dishkant implication study.

Assertion

Ref	Expression
u2lemnonb	((a →2 b)⊥ ∪ b⊥ ) = b⊥

Proof of Theorem u2lemnonb

Step	Hyp	Ref	Expression
1		df-a 39	. . . 4 ((a →2 b) ∩ b) = ((a →2 b)⊥ ∪ b⊥ )⊥
2	1	ax-r1 34	. . 3 ((a →2 b)⊥ ∪ b⊥ )⊥ = ((a →2 b) ∩ b)
3		u2lemab 593	. . 3 ((a →2 b) ∩ b) = b
4	2, 3	ax-r2 35	. 2 ((a →2 b)⊥ ∪ b⊥ )⊥ = b
5	4	con3 65	1 ((a →2 b)⊥ ∪ b⊥ ) = b⊥

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₂ wi2 14

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

This theorem depends on definitions:  df-a 39  df-i2 44

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