Theorem sseq12d

Description: An equality deduction for the subclass relationship. (Contributed by NM, 31-May-1999)

	Ref	Expression
Hypotheses	sseq1d.1	|- ( ph -> A = B )
	sseq12d.2	|- ( ph -> C = D )
Assertion	sseq12d	|- ( ph -> ( A C_ C <-> B C_ D ) )

Proof

Step	Hyp	Ref	Expression
1		sseq1d.1	|- ( ph -> A = B )
2		sseq12d.2	|- ( ph -> C = D )
3	1	sseq1d	|- ( ph -> ( A C_ C <-> B C_ C ) )
4	2	sseq2d	|- ( ph -> ( B C_ C <-> B C_ D ) )
5	3 4	bitrd	|- ( ph -> ( A C_ C <-> B C_ D ) )