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	|- ( ph -> A C_ B )
Assertion	ssdifd	|- ( ph -> ( A \ C ) C_ ( B \ C ) )

Proof

Step	Hyp	Ref	Expression
1		ssdifd.1	|- ( ph -> A C_ B )
2		ssdif	|- ( A C_ B -> ( A \ C ) C_ ( B \ C ) )
3	1 2	syl	|- ( ph -> ( A \ C ) C_ ( B \ C ) )