Theorem nfiota1

Description: Bound-variable hypothesis builder for the iota class. (Contributed by Andrew Salmon, 11-Jul-2011) (Revised by Mario Carneiro, 15-Oct-2016)

	Ref	Expression
Assertion	nfiota1	$$⊢\underset{\_}{Ⅎ}x\left(\iota x|\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		dfiota2	$$⊢\left(\iota x|\phi \right)=\bigcup \left\{y|\forall x\left(\phi \leftrightarrow x=y\right)\right\}$$
2		nfaba1	$$⊢\underset{\_}{Ⅎ}x\left\{y|\forall x\left(\phi \leftrightarrow x=y\right)\right\}$$
3	2	nfuni	$$⊢\underset{\_}{Ⅎ}x\bigcup \left\{y|\forall x\left(\phi \leftrightarrow x=y\right)\right\}$$
4	1 3	nfcxfr	$$⊢\underset{\_}{Ⅎ}x\left(\iota x|\phi \right)$$