Theorem eqeq1i

Description: Inference from equality to equivalence of equalities. (Contributed by NM, 15-Jul-1993)

	Ref	Expression
Hypothesis	eqeq1i.1	$$⊢A=B$$
Assertion	eqeq1i	$$⊢A=C\leftrightarrow B=C$$

Proof

Step	Hyp	Ref	Expression
1		eqeq1i.1	$$⊢A=B$$
2		eqeq1	$$⊢A=B\to \left(A=C\leftrightarrow B=C\right)$$
3	1 2	ax-mp	$$⊢A=C\leftrightarrow B=C$$