Metamath Proof Explorer


Theorem lenegd

Description: Negative of both sides of 'less than or equal to'. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses leidd.1 φA
ltnegd.2 φB
Assertion lenegd φABBA

Proof

Step Hyp Ref Expression
1 leidd.1 φA
2 ltnegd.2 φB
3 leneg ABABBA
4 1 2 3 syl2anc φABBA