Theorem fnafv2elrn

Description: An alternate function value belongs to the range of the function, analogous to fnfvelrn . (Contributed by AV, 2-Sep-2022)

	Ref	Expression
Assertion	fnafv2elrn	$$⊢\left(FFnA\wedge B\in A\right)\to \left(F\mathrm{\text{'}\text{'}\text{'}\text{'}}B\right)\in \mathrm{ran}F$$

Proof

Step	Hyp	Ref	Expression
1		afv2elrn	$$⊢\left(\mathrm{Fun}F\wedge B\in \mathrm{dom}F\right)\to \left(F\mathrm{\text{'}\text{'}\text{'}\text{'}}B\right)\in \mathrm{ran}F$$
2	1	funfni	$$⊢\left(FFnA\wedge B\in A\right)\to \left(F\mathrm{\text{'}\text{'}\text{'}\text{'}}B\right)\in \mathrm{ran}F$$