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Theorem nffr 4823
 Description: Bound-variable hypothesis builder for well-founded relations. (Contributed by Stefan O'Rear, 20-Jan-2015.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nffr.r
nffr.a
Assertion
Ref Expression
nffr

Proof of Theorem nffr
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-fr 4808 . 2
2 nfcv 2584 . . . . . 6
3 nffr.a . . . . . 6
42, 3nfss 3457 . . . . 5
5 nfv 1751 . . . . 5
64, 5nfan 1984 . . . 4
7 nfcv 2584 . . . . . . . 8
8 nffr.r . . . . . . . 8
9 nfcv 2584 . . . . . . . 8
107, 8, 9nfbr 4465 . . . . . . 7
1110nfn 1956 . . . . . 6
122, 11nfral 2811 . . . . 5
132, 12nfrex 2888 . . . 4
146, 13nfim 1976 . . 3
1514nfal 2003 . 2
161, 15nfxfr 1692 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370  wal 1435  wnf 1663  wnfc 2570   wne 2618  wral 2775  wrex 2776   wss 3436  c0 3761   class class class wbr 4420   wfr 4805 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ral 2780  df-rex 2781  df-rab 2784  df-v 3083  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3910  df-sn 3997  df-pr 3999  df-op 4003  df-br 4421  df-fr 4808 This theorem is referenced by:  nfwe  4825
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