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Theorem nfriota 5816
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 1459 . . 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 5815 . 2  |-  ( T. 
->  F/_ x ( iota_ y  e.  A  ph )
)
76mptru 1357 1  |-  F/_ x
( iota_ y  e.  A  ph )
Colors of variables: wff set class
Syntax hints:   T. wtru 1349   F/wnf 1453   F/_wnfc 2299   iota_crio 5806
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-sn 3587  df-uni 3795  df-iota 5158  df-riota 5807
This theorem is referenced by:  csbriotag  5819  lble  8852
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