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Metamath Proof Explorer

Theorem fovcl

Description: Closure law for an operation. (Contributed by NM, 19-Apr-2007) (Proof shortened by AV, 9-Mar-2025)

		Ref	Expression
	Hypothesis	fovcl.1	$⊢ F : R \times S ⟶ C$
	Assertion	fovcl	$⊢ (A \in R \land B \in S) \to A F B \in C$

Step	Hyp	Ref	Expression
1		fovcl.1	$⊢ F : R \times S ⟶ C$
2	1	a1i	$⊢ A \in R \to F : R \times S ⟶ C$
3	2	fovcld	$⊢ (A \in R \land A \in R \land B \in S) \to A F B \in C$
4	3	3anidm12	$⊢ (A \in R \land B \in S) \to A F B \in C$