Theorem eqtr4d

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

	Ref	Expression
Hypotheses	eqtr4d.1	$$⊢\phi \to A=B$$
	eqtr4d.2	$$⊢\phi \to C=B$$
Assertion	eqtr4d	$$⊢\phi \to A=C$$

Proof

Step	Hyp	Ref	Expression
1		eqtr4d.1	$$⊢\phi \to A=B$$
2		eqtr4d.2	$$⊢\phi \to C=B$$
3	2	eqcomd	$$⊢\phi \to B=C$$
4	1 3	eqtrd	$$⊢\phi \to A=C$$