Metamath Proof Explorer

Theorem lediv1dd

Description: Division of both sides of a less than or equal to relation by a positive number. (Contributed by Mario Carneiro, 30-May-2016)

Ref Expression
Hypotheses ltmul1d.1 φ A
ltmul1d.2 φ B
ltmul1d.3 φ C +
lediv1dd.4 φ A B
Assertion lediv1dd φ A C B C


Step Hyp Ref Expression
1 ltmul1d.1 φ A
2 ltmul1d.2 φ B
3 ltmul1d.3 φ C +
4 lediv1dd.4 φ A B
5 1 2 3 lediv1d φ A B A C B C
6 4 5 mpbid φ A C B C