Theorem sscond

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

	Ref	Expression
Hypothesis	ssdifd.1	|- ( ph -> A C_ B )
Assertion	sscond	|- ( ph -> ( C \ B ) C_ ( C \ A ) )

Proof

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