Metamath Proof Explorer


Theorem xrltnle

Description: "Less than" expressed in terms of "less than or equal to", for extended reals. (Contributed by NM, 6-Feb-2007)

Ref Expression
Assertion xrltnle A * B * A < B ¬ B A

Proof

Step Hyp Ref Expression
1 xrlenlt B * A * B A ¬ A < B
2 1 con2bid B * A * A < B ¬ B A
3 2 ancoms A * B * A < B ¬ B A