Theorem psseq1i

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

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

Proof

Step	Hyp	Ref	Expression
1		psseq1i.1	$$⊢A=B$$
2		psseq1	$$⊢A=B\to \left(A\subset C\leftrightarrow B\subset C\right)$$
3	1 2	ax-mp	$$⊢A\subset C\leftrightarrow B\subset C$$