Theorem sseq1d

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

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

Proof

Step	Hyp	Ref	Expression
1		sseq1d.1	$$⊢\phi \to A=B$$
2		sseq1	$$⊢A=B\to \left(A\subseteq C\leftrightarrow B\subseteq C\right)$$
3	1 2	syl	$$⊢\phi \to \left(A\subseteq C\leftrightarrow B\subseteq C\right)$$