Theorem u2lemle1 693

Description: L.e. to Dishkant implication.

Hypothesis

Ref	Expression
ulemle1.1	a ≤ b

Assertion

Ref	Expression
u2lemle1	(a →2 b) = 1

Proof of Theorem u2lemle1

Step	Hyp	Ref	Expression
1		ulemle1.1	. . . 4 a ≤ b
2	1	lecom 172	. . 3 a C b
3	2	u2lemc4 684	. 2 (a →2 b) = (a⊥ ∪ b)
4	1	sklem 222	. 2 (a⊥ ∪ b) = 1
5	3, 4	ax-r2 35	1 (a →2 b) = 1

Syntax hints:   = wb 1   ≤ wle 2  ^⊥ wn 4   ∪ wo 6  1wt 9   →₂ wi2 14

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-i2 44  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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