Metamath Proof Explorer


Theorem ltdiv1dd

Description: Division of both sides of 'less than' 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 +
ltdiv1dd.4 φ A < B
Assertion ltdiv1dd φ A C < B C

Proof

Step Hyp Ref Expression
1 ltmul1d.1 φ A
2 ltmul1d.2 φ B
3 ltmul1d.3 φ C +
4 ltdiv1dd.4 φ A < B
5 1 2 3 ltdiv1d φ A < B A C < B C
6 4 5 mpbid φ A C < B C