Theorem psseq12i

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

	Ref	Expression
Hypotheses	psseq1i.1	$$⊢A=B$$
	psseq12i.2	$$⊢C=D$$
Assertion	psseq12i	$$⊢A\subset C\leftrightarrow B\subset D$$

Proof

Step	Hyp	Ref	Expression
1		psseq1i.1	$$⊢A=B$$
2		psseq12i.2	$$⊢C=D$$
3	1	psseq1i	$$⊢A\subset C\leftrightarrow B\subset C$$
4	2	psseq2i	$$⊢B\subset C\leftrightarrow B\subset D$$
5	3 4	bitri	$$⊢A\subset C\leftrightarrow B\subset D$$