Theorem eqsstrrdi

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

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

Proof

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