Theorem eqtr3id

Description: An equality transitivity deduction. (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Hypotheses	eqtr3id.1	$$⊢B=A$$
	eqtr3id.2	$$⊢\phi \to B=C$$
Assertion	eqtr3id	$$⊢\phi \to A=C$$

Proof

Step	Hyp	Ref	Expression
1		eqtr3id.1	$$⊢B=A$$
2		eqtr3id.2	$$⊢\phi \to B=C$$
3	1	eqcomi	$$⊢A=B$$
4	3 2	syl5eq	$$⊢\phi \to A=C$$