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 φA
ltnegd.2 φB
ltadd1d.3 φC
leadd1dd.4 φAB
Assertion lesub1dd φACBC

Proof

Step Hyp Ref Expression
1 leidd.1 φA
2 ltnegd.2 φB
3 ltadd1d.3 φC
4 leadd1dd.4 φAB
5 1 2 3 lesub1d φABACBC
6 4 5 mpbid φACBC