Theorem nfiota 5855

Description: Bound-variable hypothesis builder for the iota class. (Contributed by NM, 23-Aug-2011.)

Hypothesis

Ref	Expression
nfiota.1	|- F/ x ph

Assertion

Ref	Expression
nfiota	|- F/_ x ( iota y ph )

Proof of Theorem nfiota

Step	Hyp	Ref	Expression
1		nftru 1730	. . 3 |- F/ y T.
2		nfiota.1	. . . 4 |- F/ x ph
3	2	a1i 11	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfiotad 5854	. 2 |- ( T. -> F/_ x ( iota y ph ) )
5	4	trud 1493	1 |- F/_ x ( iota y ph )

Syntax hints:   T. wtru 1484   F/wnf 1708   F/_wnfc 2751   iotacio 5849

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rex 2918  df-sn 4178  df-uni 4437  df-iota 5851

This theorem is referenced by:  csbiota  5881  nffv  6198  nfsum1  14420  nfsum  14421  nfcprod1  14640  nfcprod  14641