Theorem sseqtrrd

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004)

	Ref	Expression
Hypotheses	sseqtrrd.1	$$⊢\phi \to A\subseteq B$$
	sseqtrrd.2	$$⊢\phi \to C=B$$
Assertion	sseqtrrd	$$⊢\phi \to A\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		sseqtrrd.1	$$⊢\phi \to A\subseteq B$$
2		sseqtrrd.2	$$⊢\phi \to C=B$$
3	2	eqcomd	$$⊢\phi \to B=C$$
4	1 3	sseqtrd	$$⊢\phi \to A\subseteq C$$