Metamath Proof Explorer


Theorem posdifd

Description: Comparison of two numbers whose difference is positive. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses leidd.1 φ A
ltnegd.2 φ B
Assertion posdifd φ A < B 0 < B A

Proof

Step Hyp Ref Expression
1 leidd.1 φ A
2 ltnegd.2 φ B
3 posdif A B A < B 0 < B A
4 1 2 3 syl2anc φ A < B 0 < B A