Theorem u1lemle1 692

Description: L.e. to Sasaki implication.

Hypothesis

Ref	Expression
ulemle1.1	a =< b

Assertion

Ref	Expression
u1lemle1	(a ->1 b) = 1

Proof of Theorem u1lemle1

Step	Hyp	Ref	Expression
1		ulemle1.1	. . . 4 a =< b
2	1	lecom 172	. . 3 a C b
3	2	u1lemc4 683	. 2 (a ->1 b) = (a_|_ v b)
4	1	sklem 222	. 2 (a_|_ v b) = 1
5	3, 4	ax-r2 35	1 (a ->1 b) = 1

Syntax hints:   = wb 1   =< wle 2  _|_wn 4   v wo 6  1wt 9   ->1 wi1 13

This theorem is referenced by:  3vded12 797  3vded13 798

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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