Theorem eqtr2id

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

	Ref	Expression
Hypotheses	eqtr2id.1	$$⊢A=B$$
	eqtr2id.2	$$⊢\phi \to B=C$$
Assertion	eqtr2id	$$⊢\phi \to C=A$$

Proof

Step	Hyp	Ref	Expression
1		eqtr2id.1	$$⊢A=B$$
2		eqtr2id.2	$$⊢\phi \to B=C$$
3	1 2	syl5eq	$$⊢\phi \to A=C$$
4	3	eqcomd	$$⊢\phi \to C=A$$