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	$$⊢F\mathrm{defAt}A\to \left(F\mathrm{\text{'}\text{'}\text{'}\text{'}}A\right)\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		dfatafv2iota	$$⊢F\mathrm{defAt}A\to \left(F\mathrm{\text{'}\text{'}\text{'}\text{'}}A\right)=\left(\iota x|AFx\right)$$
2		iotaex	$$⊢\left(\iota x|AFx\right)\in \mathrm{V}$$
3	1 2	eqeltrdi	$$⊢F\mathrm{defAt}A\to \left(F\mathrm{\text{'}\text{'}\text{'}\text{'}}A\right)\in \mathrm{V}$$