Theorem lecon3 149

Description: Contrapositive for l.e.

Hypothesis

Ref	Expression
lecon3.1	a =< b_|_

Assertion

Ref	Expression
lecon3	b =< a_|_

Proof of Theorem lecon3

Step	Hyp	Ref	Expression
1		lecon3.1	. . . 4 a =< b_|_
2	1	lecon 146	. . 3 b_|__|_ =< a_|_
3	2	lecon2 148	. 2 a_|__|_ =< b_|_
4	3	lecon1 147	1 b =< a_|_

Syntax hints:   =< wle 2  _|_wn 4

This theorem is referenced by:  ortha 420  mhlemlem1 856  mhlem 858  govar2 877  gomaex3lem2 895  oa3to4lem6 930  oa3to4 931  oa4to6 945

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-le1 122  df-le2 123

metamath.org