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 C. C <-> B C. D )

Proof

Step	Hyp	Ref	Expression
1		psseq1i.1	|- A = B
2		psseq12i.2	|- C = D
3	1	psseq1i	|- ( A C. C <-> B C. C )
4	2	psseq2i	|- ( B C. C <-> B C. D )
5	3 4	bitri	|- ( A C. C <-> B C. D )