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Theorem nffrfor 4113
 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
nffrfor.r
nffrfor.a
nffrfor.s
Assertion
Ref Expression
nffrfor FrFor

Proof of Theorem nffrfor
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-frfor 4096 . 2 FrFor
2 nffrfor.a . . . 4
3 nfcv 2194 . . . . . . . 8
4 nffrfor.r . . . . . . . 8
5 nfcv 2194 . . . . . . . 8
63, 4, 5nfbr 3836 . . . . . . 7
7 nffrfor.s . . . . . . . 8
87nfcri 2188 . . . . . . 7
96, 8nfim 1480 . . . . . 6
102, 9nfralxy 2377 . . . . 5
117nfcri 2188 . . . . 5
1210, 11nfim 1480 . . . 4
132, 12nfralxy 2377 . . 3
142, 7nfss 2966 . . 3
1513, 14nfim 1480 . 2
161, 15nfxfr 1379 1 FrFor
 Colors of variables: wff set class Syntax hints:   wi 4  wnf 1365   wcel 1409  wnfc 2181  wral 2323   wss 2945   class class class wbr 3792  FrFor wfrfor 4092 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 This theorem is referenced by:  nffr  4114
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