Theorem u2lem2 727

Description: Lemma for unified implication study.

Assertion

Ref	Expression
u2lem2	(((a →2 b) →2 a) →2 a) = 1

Proof of Theorem u2lem2

Step	Hyp	Ref	Expression
1		df-i2 44	. 2 (((a →2 b) →2 a) →2 a) = (a ∪ (((a →2 b) →2 a)⊥ ∩ a⊥ ))
2		u2lem1n 722	. . . . . 6 ((a →2 b) →2 a)⊥ = a⊥
3	2	ran 71	. . . . 5 (((a →2 b) →2 a)⊥ ∩ a⊥ ) = (a⊥ ∩ a⊥ )
4		anidm 103	. . . . 5 (a⊥ ∩ a⊥ ) = a⊥
5	3, 4	ax-r2 35	. . . 4 (((a →2 b) →2 a)⊥ ∩ a⊥ ) = a⊥
6	5	lor 66	. . 3 (a ∪ (((a →2 b) →2 a)⊥ ∩ a⊥ )) = (a ∪ a⊥ )
7		df-t 40	. . . 4 1 = (a ∪ a⊥ )
8	7	ax-r1 34	. . 3 (a ∪ a⊥ ) = 1
9	6, 8	ax-r2 35	. 2 (a ∪ (((a →2 b) →2 a)⊥ ∩ a⊥ )) = 1
10	1, 9	ax-r2 35	1 (((a →2 b) →2 a) →2 a) = 1

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

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a5 33  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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