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Metamath Proof Explorer

Theorem xrneq12

Description: Equality theorem for the range Cartesian product. (Contributed by Peter Mazsa, 16-Dec-2020)

		Ref	Expression
	Assertion	xrneq12	$⊢ (A = B \land C = D) \to A ⋉ C = B ⋉ D$

Step	Hyp	Ref	Expression
1		xrneq1	$⊢ A = B \to A ⋉ C = B ⋉ C$
2		xrneq2	$⊢ C = D \to B ⋉ C = B ⋉ D$
3	1 2	sylan9eq	$⊢ (A = B \land C = D) \to A ⋉ C = B ⋉ D$