Theorem eqtrd

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

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

Proof

Step	Hyp	Ref	Expression
1		eqtrd.1	$$⊢\phi \to A=B$$
2		eqtrd.2	$$⊢\phi \to B=C$$
3	2	eqeq2d	$$⊢\phi \to \left(A=B\leftrightarrow A=C\right)$$
4	1 3	mpbid	$$⊢\phi \to A=C$$