Theorem eqtr2di

Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998)

	Ref	Expression
Hypotheses	eqtr2di.1	$$⊢\phi \to A=B$$
	eqtr2di.2	$$⊢B=C$$
Assertion	eqtr2di	$$⊢\phi \to C=A$$

Proof

Step	Hyp	Ref	Expression
1		eqtr2di.1	$$⊢\phi \to A=B$$
2		eqtr2di.2	$$⊢B=C$$
3	1 2	syl6eq	$$⊢\phi \to A=C$$
4	3	eqcomd	$$⊢\phi \to C=A$$