Metamath Proof Explorer


Theorem lesub1dd

Description: Subtraction from both sides of 'less than or equal to'. (Contributed by Mario Carneiro, 30-May-2016)

Ref Expression
Hypotheses leidd.1 φ A
ltnegd.2 φ B
ltadd1d.3 φ C
leadd1dd.4 φ A B
Assertion lesub1dd φ 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 leadd1dd.4 φ A B
5 1 2 3 lesub1d φ A B A C B C
6 4 5 mpbid φ A C B C