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Theorem nfiotaw 5164
Description: Bound-variable hypothesis builder for the  iota class. (Contributed by NM, 23-Aug-2011.)
Hypothesis
Ref Expression
nfiotaw.1  |-  F/ x ph
Assertion
Ref Expression
nfiotaw  |-  F/_ x
( iota y ph )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem nfiotaw
StepHypRef Expression
1 nftru 1459 . . 3  |-  F/ y T.
2 nfiotaw.1 . . . 4  |-  F/ x ph
32a1i 9 . . 3  |-  ( T. 
->  F/ x ph )
41, 3nfiotadw 5163 . 2  |-  ( T. 
->  F/_ x ( iota y ph ) )
54mptru 1357 1  |-  F/_ x
( iota y ph )
Colors of variables: wff set class
Syntax hints:   T. wtru 1349   F/wnf 1453   F/_wnfc 2299   iotacio 5158
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 3589  df-uni 3797  df-iota 5160
This theorem is referenced by:  csbiotag  5191  nffv  5506  nfsum1  11319  nfsum  11320  nfcprod1  11517  nfcprod  11518
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