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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
StepHypRef Expression
1 lecon1.1 . . 3 a' =< b'
21lecon 154 . 2 b'' =< a''
3 ax-a1 30 . 2 b = b''
4 ax-a1 30 . 2 a = a''
52, 3, 4le3tr1 140 1 b =< a
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4
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
This theorem is referenced by:  lecon2  156  lecon3  157  i3le  515  neg3antlem2  865  elimcons  868  oa4v3v  934  oa3to4lem6  950  oa4uto4g  975  oa4uto4  977
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