Metamath Proof Explorer


Theorem lesub1d

Description: Subtraction from both sides of 'less than or equal to'. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses leidd.1 φ A
ltnegd.2 φ B
ltadd1d.3 φ C
Assertion lesub1d φ A B A C B C

Proof

Step Hyp Ref Expression
1 leidd.1 φ A
2 ltnegd.2 φ B
3 ltadd1d.3 φ C
4 lesub1 A B C A B A C B C
5 1 2 3 4 syl3anc φ A B A C B C