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Theorem nfrabxy 2490
 Description: A variable not free in a wff remains so in a restricted class abstraction. (Contributed by Jim Kingdon, 19-Jul-2018.)
Hypotheses
Ref Expression
nfrabxy.1
nfrabxy.2
Assertion
Ref Expression
nfrabxy
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem nfrabxy
StepHypRef Expression
1 df-rab 2315 . 2
2 nfrabxy.2 . . . . 5
32nfcri 2172 . . . 4
4 nfrabxy.1 . . . 4
53, 4nfan 1457 . . 3
65nfab 2182 . 2
71, 6nfcxfr 2175 1
 Colors of variables: wff set class Syntax hints:   wa 97  wnf 1349   wcel 1393  cab 2026  wnfc 2165  crab 2310 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rab 2315 This theorem is referenced by:  nfdif  3065  nfin  3143  nfse  4078  mpt2xopoveq  5855  caucvgprprlemaddq  6806
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