Theorem eqsstrdi

Description: A chained subclass and equality deduction. (Contributed by Mario Carneiro, 2-Jan-2017)

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

Proof

Step	Hyp	Ref	Expression
1		eqsstrdi.1	$$⊢\phi \to A=B$$
2		eqsstrdi.2	$$⊢B\subseteq C$$
3	2	a1i	$$⊢\phi \to B\subseteq C$$
4	1 3	eqsstrd	$$⊢\phi \to A\subseteq C$$