Metamath Proof Explorer


Theorem subled

Description: Swap subtrahends in an inequality. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses leidd.1 φA
ltnegd.2 φB
ltadd1d.3 φC
subled.4 φABC
Assertion subled φACB

Proof

Step Hyp Ref Expression
1 leidd.1 φA
2 ltnegd.2 φB
3 ltadd1d.3 φC
4 subled.4 φABC
5 suble ABCABCACB
6 1 2 3 5 syl3anc φABCACB
7 4 6 mpbid φACB