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	$$⊢\phi \to A\subseteq B$$
Assertion	sscond	$$⊢\phi \to C\setminus B\subseteq C\setminus A$$

Proof

Step	Hyp	Ref	Expression
1		ssdifd.1	$$⊢\phi \to A\subseteq B$$
2		sscon	$$⊢A\subseteq B\to C\setminus B\subseteq C\setminus A$$
3	1 2	syl	$$⊢\phi \to C\setminus B\subseteq C\setminus A$$