Metamath Proof Explorer


Theorem ltsubaddd

Description: 'Less than' 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 ltsubaddd φAB<CA<C+B

Proof

Step Hyp Ref Expression
1 leidd.1 φA
2 ltnegd.2 φB
3 ltadd1d.3 φC
4 ltsubadd ABCAB<CA<C+B
5 1 2 3 4 syl3anc φAB<CA<C+B