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Theorem nffr 4114
 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 variable is distinct from all other variables.
StepHypRef Expression
1 df-frind 4097 . 2 FrFor
2 nffr.r . . . 4
3 nffr.a . . . 4
4 nfcv 2194 . . . 4
52, 3, 4nffrfor 4113 . . 3 FrFor
65nfal 1484 . 2 FrFor
71, 6nfxfr 1379 1
 Colors of variables: wff set class Syntax hints:  wal 1257  wnf 1365  wnfc 2181  FrFor wfrfor 4092   wfr 4093 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-sn 3409  df-pr 3410  df-op 3412  df-br 3793  df-frfor 4096  df-frind 4097 This theorem is referenced by:  nfwe  4120
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