Metamath Proof Explorer


Theorem lesubaddd

Description: 'Less than or equal to' relationship between subtraction and addition. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses leidd.1 φA
ltnegd.2 φB
ltadd1d.3 φC
Assertion lesubaddd φABCAC+B

Proof

Step Hyp Ref Expression
1 leidd.1 φA
2 ltnegd.2 φB
3 ltadd1d.3 φC
4 lesubadd ABCABCAC+B
5 1 2 3 4 syl3anc φABCAC+B