Theorem csbeq1d

Description: Equality deduction for proper substitution into a class. (Contributed by NM, 3-Dec-2005)

	Ref	Expression
Hypothesis	csbeq1d.1	|- ( ph -> A = B )
Assertion	csbeq1d	|- ( ph -> [_ A / x ]_ C = [_ B / x ]_ C )

Proof

Step	Hyp	Ref	Expression
1		csbeq1d.1	|- ( ph -> A = B )
2		csbeq1	|- ( A = B -> [_ A / x ]_ C = [_ B / x ]_ C )
3	1 2	syl	|- ( ph -> [_ A / x ]_ C = [_ B / x ]_ C )