Theorem u2lemnab 633

Description: Lemma for Dishkant implication study.

Assertion

Ref	Expression
u2lemnab	((a →2 b)⊥ ∩ b) = 0

Proof of Theorem u2lemnab

Step	Hyp	Ref	Expression
1		u2lemonb 618	. . 3 ((a →2 b) ∪ b⊥ ) = 1
2		oran1 83	. . 3 ((a →2 b) ∪ b⊥ ) = ((a →2 b)⊥ ∩ b)⊥
3		df-f 41	. . . . 5 0 = 1⊥
4	3	con2 64	. . . 4 0⊥ = 1
5	4	ax-r1 34	. . 3 1 = 0⊥
6	1, 2, 5	3tr2 61	. 2 ((a →2 b)⊥ ∩ b)⊥ = 0⊥
7	6	con1 63	1 ((a →2 b)⊥ ∩ b) = 0

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 9  0wf 10   →₂ wi2 14

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-i2 44

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