Theorem u1lem1 734

Description: Lemma for unified implication study. (Contributed by NM, 14-Dec-1997.)

Assertion

Ref	Expression
u1lem1	((a →1 b) →1 a) = a

Proof of Theorem u1lem1

Step	Hyp	Ref	Expression
1		u1lemc1 680	. . . 4 a C (a →1 b)
2	1	comcom 453	. . 3 (a →1 b) C a
3	2	u1lemc4 701	. 2 ((a →1 b) →1 a) = ((a →1 b)⊥ ∪ a)
4		u1lemnoa 660	. 2 ((a →1 b)⊥ ∪ a) = a
5	3, 4	ax-r2 36	1 ((a →1 b) →1 a) = a

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   →₁ wi1 12

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by:  u1lem1n  739  u1lem2  744