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Theorem nfriota 5617
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 1400 . . 3  |-  F/ y T.
2 nfriota.1 . . . 4  |-  F/ x ph
32a1i 9 . . 3  |-  ( T. 
->  F/ x ph )
4 nfriota.2 . . . 4  |-  F/_ x A
54a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
61, 3, 5nfriotadxy 5616 . 2  |-  ( T. 
->  F/_ x ( iota_ y  e.  A  ph )
)
76mptru 1298 1  |-  F/_ x
( iota_ y  e.  A  ph )
Colors of variables: wff set class
Syntax hints:   T. wtru 1290   F/wnf 1394   F/_wnfc 2215   iota_crio 5607
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-sn 3452  df-uni 3654  df-iota 4980  df-riota 5608
This theorem is referenced by:  csbriotag  5620  lble  8408
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