Metamath Proof Explorer

Theorem leadd1dd

Description: Addition to 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 leadd1dd φ A + C B + C


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 leadd1d φ A B A + C B + C
6 4 5 mpbid φ A + C B + C