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Theorem nfriota 5807
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 1454 . . 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 5806 . 2  |-  ( T. 
->  F/_ x ( iota_ y  e.  A  ph )
)
76mptru 1352 1  |-  F/_ x
( iota_ y  e.  A  ph )
Colors of variables: wff set class
Syntax hints:   T. wtru 1344   F/wnf 1448   F/_wnfc 2295   iota_crio 5797
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147
This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-rex 2450  df-sn 3582  df-uni 3790  df-iota 5153  df-riota 5798
This theorem is referenced by:  csbriotag  5810  lble  8842
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