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Theorem nffr 4858
 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 4843 . 2
2 nfcv 2619 . . . . . 6
3 nffr.a . . . . . 6
42, 3nfss 3496 . . . . 5
5 nfv 1707 . . . . 5
64, 5nfan 1928 . . . 4
7 nfcv 2619 . . . . . . . 8
8 nffr.r . . . . . . . 8
9 nfcv 2619 . . . . . . . 8
107, 8, 9nfbr 4496 . . . . . . 7
1110nfn 1901 . . . . . 6
122, 11nfral 2843 . . . . 5
132, 12nfrex 2920 . . . 4
146, 13nfim 1920 . . 3
1514nfal 1947 . 2
161, 15nfxfr 1645 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  F/wnf 1616  F/_wnfc 2605  =/=wne 2652  A.wral 2807  E.wrex 2808  C_wss 3475   c0 3784   class class class wbr 4452  Frwfr 4840 This theorem is referenced by:  nfwe  4860 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-fr 4843
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