Theorem dfatafv2ex

Description: The alternate function value at a class A is always a set if the function/class F is defined at A . (Contributed by AV, 6-Sep-2022)

	Ref	Expression
Assertion	dfatafv2ex	⊢ ( 𝐹 defAt 𝐴 → ( 𝐹 '''' 𝐴 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		dfatafv2iota	⊢ ( 𝐹 defAt 𝐴 → ( 𝐹 '''' 𝐴 ) = ( ℩ 𝑥 𝐴 𝐹 𝑥 ) )
2		iotaex	⊢ ( ℩ 𝑥 𝐴 𝐹 𝑥 ) ∈ V
3	1 2	eqeltrdi	⊢ ( 𝐹 defAt 𝐴 → ( 𝐹 '''' 𝐴 ) ∈ V )