Theorem bnj1262

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj1262.1	$$⊢A\subseteq B$$
	bnj1262.2	$$⊢\phi \to C=A$$
Assertion	bnj1262	$$⊢\phi \to C\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		bnj1262.1	$$⊢A\subseteq B$$
2		bnj1262.2	$$⊢\phi \to C=A$$
3	2 1	eqsstrdi	$$⊢\phi \to C\subseteq B$$