This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem eqeq12

Description: Equality relationship among four classes. (Contributed by NM, 3-Aug-1994) (Proof shortened by Wolf Lammen, 23-Oct-2024)

		Ref	Expression
	Assertion	eqeq12	$⊢ (A = B \land C = D) \to (A = C \leftrightarrow B = D)$

Step	Hyp	Ref	Expression
1		id	$⊢ A = B \to A = B$
2		id	$⊢ C = D \to C = D$
3	1 2	eqeqan12d	$⊢ (A = B \land C = D) \to (A = C \leftrightarrow B = D)$