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Theorem nfpr 3420
 Description: Bound-variable hypothesis builder for unordered pairs. (Contributed by NM, 14-Nov-1995.)
Hypotheses
Ref Expression
nfpr.1
nfpr.2
Assertion
Ref Expression
nfpr

Proof of Theorem nfpr
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfpr2 3394 . 2
2 nfpr.1 . . . . 5
32nfeq2 2189 . . . 4
4 nfpr.2 . . . . 5
54nfeq2 2189 . . . 4
63, 5nfor 1466 . . 3
76nfab 2182 . 2
81, 7nfcxfr 2175 1
 Colors of variables: wff set class Syntax hints:   wo 629   wceq 1243  cab 2026  wnfc 2165  cpr 3376 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-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 This theorem is referenced by:  nfsn  3430  nfop  3565
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