Metamath Proof Explorer


Theorem ltaddsub2d

Description: 'Less than' relationship between subtraction and addition. (Contributed by Mario Carneiro, 29-Dec-2016)

Ref Expression
Hypotheses leidd.1 φ A
ltnegd.2 φ B
ltadd1d.3 φ C
Assertion ltaddsub2d φ A + B < C B < C A

Proof

Step Hyp Ref Expression
1 leidd.1 φ A
2 ltnegd.2 φ B
3 ltadd1d.3 φ C
4 ltaddsub2 A B C A + B < C B < C A
5 1 2 3 4 syl3anc φ A + B < C B < C A