Theorem lecon1 147

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 146	. 2 b⊥ ⊥ ≤ a⊥ ⊥
3		ax-a1 29	. 2 b = b⊥ ⊥
4		ax-a1 29	. 2 a = a⊥ ⊥
5	2, 3, 4	le3tr1 132	1 b ≤ a

Syntax hints:   ≤ wle 2  ^⊥ wn 4

This theorem is referenced by:  lecon2 148  lecon3 149  i3le 497  neg3antlem2 847  elimcons 850  oa4v3v 914  oa3to4lem6 930  oa4uto4g 955  oa4uto4 957

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

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