Theorem psseq12d

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

	Ref	Expression
Hypotheses	psseq1d.1	|- ( ph -> A = B )
	psseq12d.2	|- ( ph -> C = D )
Assertion	psseq12d	|- ( ph -> ( A C. C <-> B C. D ) )

Proof

Step	Hyp	Ref	Expression
1		psseq1d.1	|- ( ph -> A = B )
2		psseq12d.2	|- ( ph -> C = D )
3	1	psseq1d	|- ( ph -> ( A C. C <-> B C. C ) )
4	2	psseq2d	|- ( ph -> ( B C. C <-> B C. D ) )
5	3 4	bitrd	|- ( ph -> ( A C. C <-> B C. D ) )