Theorem fmpod

Description: Domain and codomain of the mapping operation; deduction form. (Contributed by Zhi Wang, 30-Sep-2025)

	Ref	Expression
Hypotheses	fmpodg.1	|- ( ph -> F = ( x e. A , y e. B |-> C ) )
	fmpodg.2	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> C e. S )
Assertion	fmpod	|- ( ph -> F : ( A X. B ) --> S )

Proof

Step	Hyp	Ref	Expression
1		fmpodg.1	|- ( ph -> F = ( x e. A , y e. B |-> C ) )
2		fmpodg.2	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> C e. S )
3		eqidd	|- ( ph -> ( A X. B ) = ( A X. B ) )
4	1 2 3	fmpodg	|- ( ph -> F : ( A X. B ) --> S )