Theorem syl5eq

Description: An equality transitivity deduction. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	syl5eq.1	$$⊢A=B$$
	syl5eq.2	$$⊢\phi \to B=C$$
Assertion	syl5eq	$$⊢\phi \to A=C$$

Proof

Step	Hyp	Ref	Expression
1		syl5eq.1	$$⊢A=B$$
2		syl5eq.2	$$⊢\phi \to B=C$$
3	1	a1i	$$⊢\phi \to A=B$$
4	3 2	eqtrd	$$⊢\phi \to A=C$$