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Theorem nfriota 6330
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 1544 . . 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 6329 . 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 1534   F/_wnfc 2419   iota_crio 6313
This theorem is referenced by:  csbriotag  6333  riotasvd  6363  riotasvdOLD  6364  riotasv2d  6365  riotasv2dOLD  6366  riotasv2s  6367  riotasv3dOLD  6370  nfoi  7245  lble  9722  cdleme26ee  31171  cdleme31sn1  31192  cdlemefs32sn1aw  31225  cdleme43fsv1snlem  31231  cdleme41sn3a  31244  cdleme32d  31255  cdleme32f  31257  cdleme40m  31278  cdleme40n  31279  cdlemk36  31724  cdlemk38  31726  cdlemkid  31747  cdlemk19x  31754  cdlemk11t  31757
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-reu 2563  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-riota 6320
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