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Theorem nfrecs 6635
 Description: Bound-variable hypothesis builder for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.)
Hypothesis
Ref Expression
nfrecs.f
Assertion
Ref Expression
nfrecs recs

Proof of Theorem nfrecs
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-recs 6633 . 2 recs
2 nfcv 2572 . . . . 5
3 nfv 1629 . . . . . 6
4 nfcv 2572 . . . . . . 7
5 nfrecs.f . . . . . . . . 9
6 nfcv 2572 . . . . . . . . 9
75, 6nffv 5735 . . . . . . . 8
87nfeq2 2583 . . . . . . 7
94, 8nfral 2759 . . . . . 6
103, 9nfan 1846 . . . . 5
112, 10nfrex 2761 . . . 4
1211nfab 2576 . . 3
1312nfuni 4021 . 2
141, 13nfcxfr 2569 1 recs
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652  cab 2422  wnfc 2559  wral 2705  wrex 2706  cuni 4015  con0 4581   cres 4880   wfn 5449  cfv 5454  recscrecs 6632 This theorem is referenced by:  nfrdg  6672  nfoi  7483  aomclem8  27136 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-recs 6633
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