Metamath Proof Explorer


Theorem lenegcon2d

Description: Contraposition of negative in 'less than or equal to'. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses leidd.1 φ A
ltnegd.2 φ B
lenegcon2d.3 φ A B
Assertion lenegcon2d φ B A

Proof

Step Hyp Ref Expression
1 leidd.1 φ A
2 ltnegd.2 φ B
3 lenegcon2d.3 φ A B
4 lenegcon2 A B A B B A
5 1 2 4 syl2anc φ A B B A
6 3 5 mpbid φ B A