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Theorem nfriota 5477
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 1355 . . 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 5476 . 2  |-  ( T. 
->  F/_ x ( iota_ y  e.  A  ph )
)
76trud 1252 1  |-  F/_ x
( iota_ y  e.  A  ph )
Colors of variables: wff set class
Syntax hints:   T. wtru 1244   F/wnf 1349   F/_wnfc 2165   iota_crio 5467
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-sn 3381  df-uni 3581  df-iota 4867  df-riota 5468
This theorem is referenced by:  csbriotag  5480
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