Theorem eqtr2d

Description: An equality transitivity deduction. (Contributed by NM, 18-Oct-1999)

	Ref	Expression
Hypotheses	eqtr2d.1	|- ( ph -> A = B )
	eqtr2d.2	|- ( ph -> B = C )
Assertion	eqtr2d	|- ( ph -> C = A )

Proof

Step	Hyp	Ref	Expression
1		eqtr2d.1	|- ( ph -> A = B )
2		eqtr2d.2	|- ( ph -> B = C )
3	1 2	eqtrd	|- ( ph -> A = C )
4	3	eqcomd	|- ( ph -> C = A )