Theorem eqeq12i

Description: A useful inference for substituting definitions into an equality. (Contributed by NM, 15-Jul-1993) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 20-Nov-2019)

	Ref	Expression
Hypotheses	eqeq12i.1	$$⊢A=B$$
	eqeq12i.2	$$⊢C=D$$
Assertion	eqeq12i	$$⊢A=C\leftrightarrow B=D$$

Proof

Step	Hyp	Ref	Expression
1		eqeq12i.1	$$⊢A=B$$
2		eqeq12i.2	$$⊢C=D$$
3	1	eqeq1i	$$⊢A=C\leftrightarrow B=C$$
4	2	eqeq2i	$$⊢B=C\leftrightarrow B=D$$
5	3 4	bitri	$$⊢A=C\leftrightarrow B=D$$