Theorem psseq2d

Description: An equality deduction for the proper subclass relationship. (Contributed by NM, 9-Jun-2004)

	Ref	Expression
Hypothesis	psseq1d.1	$$⊢\phi \to A=B$$
Assertion	psseq2d	$$⊢\phi \to \left(C\subset A\leftrightarrow C\subset B\right)$$

Proof

Step	Hyp	Ref	Expression
1		psseq1d.1	$$⊢\phi \to A=B$$
2		psseq2	$$⊢A=B\to \left(C\subset A\leftrightarrow C\subset B\right)$$
3	1 2	syl	$$⊢\phi \to \left(C\subset A\leftrightarrow C\subset B\right)$$