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Theorem nfpr 3581
 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 3551 . 2
2 nfpr.1 . . . . 5
32nfeq2 2294 . . . 4
4 nfpr.2 . . . . 5
54nfeq2 2294 . . . 4
63, 5nfor 1554 . . 3
76nfab 2287 . 2
81, 7nfcxfr 2279 1
 Colors of variables: wff set class Syntax hints:   wo 698   wceq 1332  cab 2126  wnfc 2269  cpr 3533 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3080  df-sn 3538  df-pr 3539 This theorem is referenced by:  nfsn  3591  nfop  3729
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