Theorem eqtr4d

Description: An equality transitivity equality deduction. (Contributed by NM, 18-Jul-1995)

	Ref	Expression
Hypotheses	eqtr4d.1	|- ( ph -> A = B )
	eqtr4d.2	|- ( ph -> C = B )
Assertion	eqtr4d	|- ( ph -> A = C )

Proof

Step	Hyp	Ref	Expression
1		eqtr4d.1	|- ( ph -> A = B )
2		eqtr4d.2	|- ( ph -> C = B )
3	2	eqcomd	|- ( ph -> B = C )
4	1 3	eqtrd	|- ( ph -> A = C )