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Theorem nfiota 5223
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
StepHypRef Expression
1 nftru 1541 . . 3  |-  F/ y  T.
2 nfiota.1 . . . 4  |-  F/ x ph
32a1i 10 . . 3  |-  (  T. 
->  F/ x ph )
41, 3nfiotad 5222 . 2  |-  (  T. 
->  F/_ x ( iota y ph ) )
54trud 1314 1  |-  F/_ x
( iota y ph )
Colors of variables: wff set class
Syntax hints:    T. wtru 1307   F/wnf 1531   F/_wnfc 2406   iotacio 5217
This theorem is referenced by:  csbiotag  5248  nffv  5532  nfsum1  12163  nfsum  12164
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-sn 3646  df-uni 3828  df-iota 5219
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