Theorem eqtrdi

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

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

Proof

Step	Hyp	Ref	Expression
1		eqtrdi.1	$$⊢\phi \to A=B$$
2		eqtrdi.2	$$⊢B=C$$
3	2	a1i	$$⊢\phi \to B=C$$
4	1 3	eqtrd	$$⊢\phi \to A=C$$