Metamath Proof Explorer


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
|- F/_ x ( iota x ph )

Proof

Step Hyp Ref Expression
1 dfiota2
 |-  ( iota x ph ) = U. { y | A. x ( ph <-> x = y ) }
2 nfaba1
 |-  F/_ x { y | A. x ( ph <-> x = y ) }
3 2 nfuni
 |-  F/_ x U. { y | A. x ( ph <-> x = y ) }
4 1 3 nfcxfr
 |-  F/_ x ( iota x ph )