Theorem eqtr4di

Description: An equality transitivity deduction. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	eqtr4di.1	$$⊢\phi \to A=B$$
	eqtr4di.2	$$⊢C=B$$
Assertion	eqtr4di	$$⊢\phi \to A=C$$

Proof

Step	Hyp	Ref	Expression
1		eqtr4di.1	$$⊢\phi \to A=B$$
2		eqtr4di.2	$$⊢C=B$$
3	2	eqcomi	$$⊢B=C$$
4	1 3	eqtrdi	$$⊢\phi \to A=C$$