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Theorem nfriota 6559
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 1563 . . 3  |-  F/ y  T.
2 nfriota.1 . . . 4  |-  F/ x ph
32a1i 11 . . 3  |-  (  T. 
->  F/ x ph )
4 nfriota.2 . . . 4  |-  F/_ x A
54a1i 11 . . 3  |-  (  T. 
->  F/_ x A )
61, 3, 5nfriotad 6558 . 2  |-  (  T. 
->  F/_ x ( iota_ y  e.  A ph )
)
76trud 1332 1  |-  F/_ x
( iota_ y  e.  A ph )
Colors of variables: wff set class
Syntax hints:    T. wtru 1325   F/wnf 1553   F/_wnfc 2559   iota_crio 6542
This theorem is referenced by:  csbriotag  6562  riotasvd  6592  riotasvdOLD  6593  riotasv2d  6594  riotasv2dOLD  6595  riotasv2s  6596  riotasv3dOLD  6599  nfoi  7483  lble  9960  cdleme26ee  31157  cdleme31sn1  31178  cdlemefs32sn1aw  31211  cdleme43fsv1snlem  31217  cdleme41sn3a  31230  cdleme32d  31241  cdleme32f  31243  cdleme40m  31264  cdleme40n  31265  cdlemk36  31710  cdlemk38  31712  cdlemkid  31733  cdlemk19x  31740  cdlemk11t  31743
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-reu 2712  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-riota 6549
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