Theorem sseq2d

Description: An equality deduction for the subclass relationship. (Contributed by NM, 14-Aug-1994)

	Ref	Expression
Hypothesis	sseq1d.1	$$⊢\phi \to A=B$$
Assertion	sseq2d	$$⊢\phi \to \left(C\subseteq A\leftrightarrow C\subseteq B\right)$$

Proof

Step	Hyp	Ref	Expression
1		sseq1d.1	$$⊢\phi \to A=B$$
2		sseq2	$$⊢A=B\to \left(C\subseteq A\leftrightarrow C\subseteq B\right)$$
3	1 2	syl	$$⊢\phi \to \left(C\subseteq A\leftrightarrow C\subseteq B\right)$$