Theorem eqtr3d

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

	Ref	Expression
Hypotheses	eqtr3d.1	|- ( ph -> A = B )
	eqtr3d.2	|- ( ph -> A = C )
Assertion	eqtr3d	|- ( ph -> B = C )

Proof

Step	Hyp	Ref	Expression
1		eqtr3d.1	|- ( ph -> A = B )
2		eqtr3d.2	|- ( ph -> A = C )
3	1	eqcomd	|- ( ph -> B = A )
4	3 2	eqtrd	|- ( ph -> B = C )