Theorem u2lem2 745

Description: Lemma for unified implication study. (Contributed by NM, 16-Dec-1997.)

Assertion

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

Proof of Theorem u2lem2

Step	Hyp	Ref	Expression
1		df-i2 45	. 2 (((a →2 b) →2 a) →2 a) = (a ∪ (((a →2 b) →2 a)⊥ ∩ a⊥ ))
2		u2lem1n 740	. . . . . 6 ((a →2 b) →2 a)⊥ = a⊥
3	2	ran 78	. . . . 5 (((a →2 b) →2 a)⊥ ∩ a⊥ ) = (a⊥ ∩ a⊥ )
4		anidm 111	. . . . 5 (a⊥ ∩ a⊥ ) = a⊥
5	3, 4	ax-r2 36	. . . 4 (((a →2 b) →2 a)⊥ ∩ a⊥ ) = a⊥
6	5	lor 70	. . 3 (a ∪ (((a →2 b) →2 a)⊥ ∩ a⊥ )) = (a ∪ a⊥ )
7		df-t 41	. . . 4 1 = (a ∪ a⊥ )
8	7	ax-r1 35	. . 3 (a ∪ a⊥ ) = 1
9	6, 8	ax-r2 36	. 2 (a ∪ (((a →2 b) →2 a)⊥ ∩ a⊥ )) = 1
10	1, 9	ax-r2 36	1 (((a →2 b) →2 a) →2 a) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   →₂ wi2 13

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i2 45

This theorem is referenced by: (None)