Metamath Proof Explorer


Theorem nfiota

Description: Bound-variable hypothesis builder for the iota class. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfiotaw when possible. (Contributed by NM, 23-Aug-2011) (New usage is discouraged.)

Ref Expression
Hypothesis nfiota.1
|- F/ x ph
Assertion nfiota
|- F/_ x ( iota y ph )

Proof

Step Hyp Ref Expression
1 nfiota.1
 |-  F/ x ph
2 nftru
 |-  F/ y T.
3 1 a1i
 |-  ( T. -> F/ x ph )
4 2 3 nfiotad
 |-  ( T. -> F/_ x ( iota y ph ) )
5 4 mptru
 |-  F/_ x ( iota y ph )