Theorem u3lemle1 712

Description: L.e. to Kalmbach implication. (Contributed by NM, 11-Jan-1998.)

Hypothesis

Ref	Expression
ulemle1.1	a ≤ b

Assertion

Ref	Expression
u3lemle1	(a →3 b) = 1

Proof of Theorem u3lemle1

Step	Hyp	Ref	Expression
1		ulemle1.1	. . . 4 a ≤ b
2	1	lecom 180	. . 3 a C b
3	2	u3lemc4 703	. 2 (a →3 b) = (a⊥ ∪ b)
4	1	sklem 230	. 2 (a⊥ ∪ b) = 1
5	3, 4	ax-r2 36	1 (a →3 b) = 1

Syntax hints:   = wb 1   ≤ wle 2  ^⊥ wn 4   ∪ wo 6  1wt 8   →₃ wi3 14

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-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by:  u3lem14mp  794