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Theorem nfrecs 7675
Description: Bound-variable hypothesis builder for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.)
Hypothesis
Ref Expression
nfrecs.f 𝑥𝐹
Assertion
Ref Expression
nfrecs 𝑥recs(𝐹)

Proof of Theorem nfrecs
StepHypRef Expression
1 df-recs 7672 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
2 nfcv 2907 . . 3 𝑥 E
3 nfcv 2907 . . 3 𝑥On
4 nfrecs.f . . 3 𝑥𝐹
52, 3, 4nfwrecs 7612 . 2 𝑥wrecs( E , On, 𝐹)
61, 5nfcxfr 2905 1 𝑥recs(𝐹)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2894   E cep 5189  Oncon0 5908  wrecscwrecs 7609  recscrecs 7671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-13 2352  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-3an 1109  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-nfc 2896  df-ral 3060  df-rex 3061  df-rab 3064  df-v 3352  df-dif 3735  df-un 3737  df-in 3739  df-ss 3746  df-nul 4080  df-if 4244  df-sn 4335  df-pr 4337  df-op 4341  df-uni 4595  df-br 4810  df-opab 4872  df-xp 5283  df-cnv 5285  df-dm 5287  df-rn 5288  df-res 5289  df-ima 5290  df-pred 5865  df-iota 6031  df-fv 6076  df-wrecs 7610  df-recs 7672
This theorem is referenced by:  nfrdg  7714  nfoi  8626  aomclem8  38308
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