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Theorem nfop 3565
 Description: Bound-variable hypothesis builder for ordered pairs. (Contributed by NM, 14-Nov-1995.)
Hypotheses
Ref Expression
nfop.1
nfop.2
Assertion
Ref Expression
nfop

Proof of Theorem nfop
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-op 3384 . 2
2 nfop.1 . . . . 5
32nfel1 2188 . . . 4
4 nfop.2 . . . . 5
54nfel1 2188 . . . 4
62nfsn 3430 . . . . . 6
72, 4nfpr 3420 . . . . . 6
86, 7nfpr 3420 . . . . 5
98nfcri 2172 . . . 4
103, 5, 9nf3an 1458 . . 3
1110nfab 2182 . 2
121, 11nfcxfr 2175 1
 Colors of variables: wff set class Syntax hints:   w3a 885   wcel 1393  cab 2026  wnfc 2165  cvv 2557  csn 3375  cpr 3376  cop 3378 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384 This theorem is referenced by:  nfopd  3566  moop2  3988  fliftfuns  5438  dfmpt2  5844  qliftfuns  6190  caucvgprprlemaddq  6806  nfiseq  9218
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