Metamath Proof Explorer


Theorem ssdifd

Description: If A is contained in B , then ( A \ C ) is contained in ( B \ C ) . Deduction form of ssdif . (Contributed by David Moews, 1-May-2017)

Ref Expression
Hypothesis ssdifd.1 φAB
Assertion ssdifd φACBC

Proof

Step Hyp Ref Expression
1 ssdifd.1 φAB
2 ssdif ABACBC
3 1 2 syl φACBC