Theorem u1lem9ab 779

Description: Lemma used in study of orthoarguesian law. (Contributed by NM, 27-Dec-1998.)

Assertion

Ref	Expression
u1lem9ab	(a⊥ →1 b)⊥ ≤ (a →1 b)

Proof of Theorem u1lem9ab

Step	Hyp	Ref	Expression
1		u1lem9a 777	. 2 (a⊥ →1 b)⊥ ≤ a⊥
2		u1lem9b 778	. 2 a⊥ ≤ (a →1 b)
3	1, 2	letr 137	1 (a⊥ →1 b)⊥ ≤ (a →1 b)

Syntax hints:   ≤ wle 2  ^⊥ wn 4   →₁ wi1 12

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-i1 44  df-le1 130  df-le2 131

This theorem is referenced by:  3vcom  813  oa3-u1  991  oa3-u2  992