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 <-> B = D )

Proof

Step	Hyp	Ref	Expression
1		eqeq12i.1	|- A = B
2		eqeq12i.2	|- C = D
3	1	eqeq1i	|- ( A = C <-> B = C )
4	2	eqeq2i	|- ( B = C <-> B = D )
5	3 4	bitri	|- ( A = C <-> B = D )