Theorem u1lem12 763

Description: Lemma used in study of orthoarguesian law.

Assertion

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

Proof of Theorem u1lem12

Step	Hyp	Ref	Expression
1		ax-a1 29	. . . 4 a = a⊥ ⊥
2	1	ud1lem0b 248	. . 3 (a →1 b) = (a⊥ ⊥ →1 b)
3	2	ud1lem0b 248	. 2 ((a →1 b) →1 b) = ((a⊥ ⊥ →1 b) →1 b)
4		u1lem11 762	. 2 ((a⊥ ⊥ →1 b) →1 b) = (a⊥ →1 b)
5	3, 4	ax-r2 35	1 ((a →1 b) →1 b) = (a⊥ →1 b)

Syntax hints:   = wb 1  ^⊥ wn 4   →₁ wi1 13

This theorem is referenced by:  sac 817  oa4gto4u 956

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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