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Theorem nfriota 6314
Description: A variable not free in a wff remains so in a restricted iota descriptor. (Contributed by NM, 12-Oct-2011.)
Hypotheses
Ref Expression
nfriota.1  |-  F/ x ph
nfriota.2  |-  F/_ x A
Assertion
Ref Expression
nfriota  |-  F/_ x
( iota_ y  e.  A ph )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)    A( x, y)

Proof of Theorem nfriota
StepHypRef Expression
1 nftru 1541 . . 3  |-  F/ y  T.
2 nfriota.1 . . . 4  |-  F/ x ph
32a1i 10 . . 3  |-  (  T. 
->  F/ x ph )
4 nfriota.2 . . . 4  |-  F/_ x A
54a1i 10 . . 3  |-  (  T. 
->  F/_ x A )
61, 3, 5nfriotad 6313 . 2  |-  (  T. 
->  F/_ x ( iota_ y  e.  A ph )
)
76trud 1314 1  |-  F/_ x
( iota_ y  e.  A ph )
Colors of variables: wff set class
Syntax hints:    T. wtru 1307   F/wnf 1531   F/_wnfc 2406   iota_crio 6297
This theorem is referenced by:  csbriotag  6317  riotasvd  6347  riotasvdOLD  6348  riotasv2d  6349  riotasv2dOLD  6350  riotasv2s  6351  riotasv3dOLD  6354  nfoi  7229  lble  9706  cdleme26ee  30549  cdleme31sn1  30570  cdlemefs32sn1aw  30603  cdleme43fsv1snlem  30609  cdleme41sn3a  30622  cdleme32d  30633  cdleme32f  30635  cdleme40m  30656  cdleme40n  30657  cdlemk36  31102  cdlemk38  31104  cdlemkid  31125  cdlemk19x  31132  cdlemk11t  31135
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-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-reu 2550  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-riota 6304
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