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 φ A
ltnegd.2 φ B
ltadd1d.3 φ C
Assertion ltsubaddd φ A B < C A < C + B

Proof

Step Hyp Ref Expression
1 leidd.1 φ A
2 ltnegd.2 φ B
3 ltadd1d.3 φ C
4 ltsubadd A B C A B < C A < C + B
5 1 2 3 4 syl3anc φ A B < C A < C + B