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Theorem nfpr 3857
 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 3832 . 2
2 nfpr.1 . . . . 5
32nfeq2 2585 . . . 4
4 nfpr.2 . . . . 5
54nfeq2 2585 . . . 4
63, 5nfor 1859 . . 3
76nfab 2578 . 2
81, 7nfcxfr 2571 1
 Colors of variables: wff set class Syntax hints:   wo 359   wceq 1653  cab 2424  wnfc 2561  cpr 3817 This theorem is referenced by:  nfsn  3868  nfop  4002  nfaltop  25830 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-sn 3822  df-pr 3823
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