Theorem eqtr3d

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

	Ref	Expression
Hypotheses	eqtr3d.1	$$⊢\phi \to A=B$$
	eqtr3d.2	$$⊢\phi \to A=C$$
Assertion	eqtr3d	$$⊢\phi \to B=C$$

Proof

Step	Hyp	Ref	Expression
1		eqtr3d.1	$$⊢\phi \to A=B$$
2		eqtr3d.2	$$⊢\phi \to A=C$$
3	1	eqcomd	$$⊢\phi \to B=A$$
4	3 2	eqtrd	$$⊢\phi \to B=C$$