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Theorem nfop 3556
Description: Bound-variable hypothesis builder for ordered pairs. (Contributed by NM, 14-Nov-1995.)
Hypotheses
Ref Expression
nfop.1  F/_
nfop.2  F/_
Assertion
Ref Expression
nfop  F/_ <. ,  >.

Proof of Theorem nfop
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-op 3376 . 2  <. ,  >.  {  |  _V  _V  { { } ,  { ,  } } }
2 nfop.1 . . . . 5  F/_
32nfel1 2185 . . . 4  F/  _V
4 nfop.2 . . . . 5  F/_
54nfel1 2185 . . . 4  F/  _V
62nfsn 3421 . . . . . 6  F/_ { }
72, 4nfpr 3411 . . . . . 6  F/_ { ,  }
86, 7nfpr 3411 . . . . 5  F/_ { { } ,  { ,  } }
98nfcri 2169 . . . 4  F/  { { } ,  { ,  } }
103, 5, 9nf3an 1455 . . 3  F/  _V  _V  { { } ,  { ,  } }
1110nfab 2179 . 2  F/_ {  |  _V  _V 
{ { } ,  { ,  } } }
121, 11nfcxfr 2172 1  F/_ <. ,  >.
Colors of variables: wff set class
Syntax hints:   w3a 884   wcel 1390   {cab 2023   F/_wnfc 2162   _Vcvv 2551   {csn 3367   {cpr 3368   <.cop 3370
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-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-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376
This theorem is referenced by:  nfopd  3557  moop2  3979  fliftfuns  5381  dfmpt2  5786  qliftfuns  6126  nfiseq  8858
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