Theorem lecon1 155

Description: Contrapositive for l.e.

Hypothesis

Ref	Expression
lecon1.1	a' =< b'

Assertion

Ref	Expression
lecon1	b =< a

Proof of Theorem lecon1

Step	Hyp	Ref	Expression
1		lecon1.1	. . 3 a' =< b'
2	1	lecon 154	. 2 b'' =< a''
3		ax-a1 30	. 2 b = b''
4		ax-a1 30	. 2 a = a''
5	2, 3, 4	le3tr1 140	1 b =< a

Syntax hints:   =< wle 2  'wn 4

This theorem is referenced by:  lecon2 156  lecon3 157  i3le 515  neg3antlem2 865  elimcons 868  oa4v3v 934  oa3to4lem6 950  oa4uto4g 975  oa4uto4 977

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-le1 130  df-le2 131

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