Theorem u1lem12 781

Description: Lemma used in study of orthoarguesian law. Equation 4.12 of [MegPav2000] p. 23. (Contributed by NM, 28-Dec-1998.)

Assertion

Ref	Expression
u1lem12	((a →1 b) →1 b) = (a⊥ →1 b)

Proof of Theorem u1lem12

Step	Hyp	Ref	Expression
1		ax-a1 30	. . . 4 a = a⊥ ⊥
2	1	ud1lem0b 256	. . 3 (a →1 b) = (a⊥ ⊥ →1 b)
3	2	ud1lem0b 256	. 2 ((a →1 b) →1 b) = ((a⊥ ⊥ →1 b) →1 b)
4		u1lem11 780	. 2 ((a⊥ ⊥ →1 b) →1 b) = (a⊥ →1 b)
5	3, 4	ax-r2 36	1 ((a →1 b) →1 b) = (a⊥ →1 b)

Syntax hints:   = wb 1  ^⊥ wn 4   →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:  sac  835  oa4gto4u  976  lem4.6.4  1086