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Theorem nfif 3350
Description: Bound-variable hypothesis builder for a conditional operator. (Contributed by NM, 16-Feb-2005.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Hypotheses
Ref Expression
nfif.1  F/
nfif.2  F/_
nfif.3  F/_
Assertion
Ref Expression
nfif  F/_ if ,  ,

Proof of Theorem nfif
StepHypRef Expression
1 nfif.1 . . . 4  F/
21a1i 9 . . 3  F/
3 nfif.2 . . . 4  F/_
43a1i 9 . . 3  F/_
5 nfif.3 . . . 4  F/_
65a1i 9 . . 3  F/_
72, 4, 6nfifd 3349 . 2  F/_ if ,  ,
87trud 1251 1  F/_ if ,  ,
Colors of variables: wff set class
Syntax hints:   wtru 1243   F/wnf 1346   F/_wnfc 2162   ifcif 3325
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-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-if 3326
This theorem is referenced by: (None)
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