Theorem eqtr2d

Description: An equality transitivity deduction. (Contributed by NM, 18-Oct-1999)

	Ref	Expression
Hypotheses	eqtr2d.1	$$⊢\phi \to A=B$$
	eqtr2d.2	$$⊢\phi \to B=C$$
Assertion	eqtr2d	$$⊢\phi \to C=A$$

Proof

Step	Hyp	Ref	Expression
1		eqtr2d.1	$$⊢\phi \to A=B$$
2		eqtr2d.2	$$⊢\phi \to B=C$$
3	1 2	eqtrd	$$⊢\phi \to A=C$$
4	3	eqcomd	$$⊢\phi \to C=A$$