Theorem sseqtrrdi

Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004)

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

Proof

Step	Hyp	Ref	Expression
1		sseqtrrdi.1	$$⊢\phi \to A\subseteq B$$
2		sseqtrrdi.2	$$⊢C=B$$
3	2	eqcomi	$$⊢B=C$$
4	1 3	sseqtrdi	$$⊢\phi \to A\subseteq C$$