Theorem psseq2i

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

	Ref	Expression
Hypothesis	psseq1i.1	$$⊢A=B$$
Assertion	psseq2i	$$⊢C\subset A\leftrightarrow C\subset B$$

Proof

Step	Hyp	Ref	Expression
1		psseq1i.1	$$⊢A=B$$
2		psseq2	$$⊢A=B\to \left(C\subset A\leftrightarrow C\subset B\right)$$
3	1 2	ax-mp	$$⊢C\subset A\leftrightarrow C\subset B$$