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Theorem nfriota 5739
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 1442 . . 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 5738 . 2  |-  ( T. 
->  F/_ x ( iota_ y  e.  A  ph )
)
76mptru 1340 1  |-  F/_ x
( iota_ y  e.  A  ph )
Colors of variables: wff set class
Syntax hints:   T. wtru 1332   F/wnf 1436   F/_wnfc 2268   iota_crio 5729
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-sn 3533  df-uni 3737  df-iota 5088  df-riota 5730
This theorem is referenced by:  csbriotag  5742  lble  8712
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