Theorem lecon2 148

Description: Contrapositive for l.e.

Hypothesis

Ref	Expression
lecon2.1	a⊥ ≤ b

Assertion

Ref	Expression
lecon2	b⊥ ≤ a

Proof of Theorem lecon2

Step	Hyp	Ref	Expression
1		lecon2.1	. . 3 a⊥ ≤ b
2		ax-a1 29	. . 3 b = b⊥ ⊥
3	1, 2	lbtr 131	. 2 a⊥ ≤ b⊥ ⊥
4	3	lecon1 147	1 b⊥ ≤ a

Syntax hints:   ≤ wle 2  ^⊥ wn 4

This theorem is referenced by:  lecon3 149  cancellem 873  kb10iii 875

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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