Theorem eqtr3di

Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998)

	Ref	Expression
Hypotheses	eqtr3di.1	$$⊢\phi \to A=B$$
	eqtr3di.2	$$⊢A=C$$
Assertion	eqtr3di	$$⊢\phi \to B=C$$

Proof

Step	Hyp	Ref	Expression
1		eqtr3di.1	$$⊢\phi \to A=B$$
2		eqtr3di.2	$$⊢A=C$$
3	2	eqcomi	$$⊢C=A$$
4	3 1	eqtr2id	$$⊢\phi \to B=C$$