Metamath Proof Explorer


Theorem leadd2d

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

Ref Expression
Hypotheses leidd.1 φA
ltnegd.2 φB
ltadd1d.3 φC
Assertion leadd2d φABC+AC+B

Proof

Step Hyp Ref Expression
1 leidd.1 φA
2 ltnegd.2 φB
3 ltadd1d.3 φC
4 leadd2 ABCABC+AC+B
5 1 2 3 4 syl3anc φABC+AC+B