Theorem lecon3 157

Description: Contrapositive for l.e. (Contributed by NM, 19-Dec-1998.)

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 154	. . 3 b⊥ ⊥ ≤ a⊥
3	2	lecon2 156	. 2 a⊥ ⊥ ≤ b⊥
4	3	lecon1 155	1 b ≤ a⊥

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:  ortha  438  mhlemlem1  874  mhlem  876  e2ast2  894  e2astlem1  895  govar2  897  gomaex3lem2  915  oa3to4lem6  950  oa3to4  951  oa4to6  965  oa3moa3  1029