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Theorem nfrecs 7335
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 7332 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
2 nfcv 2750 . . 3 𝑥 E
3 nfcv 2750 . . 3 𝑥On
4 nfrecs.f . . 3 𝑥𝐹
52, 3, 4nfwrecs 7273 . 2 𝑥wrecs( E , On, 𝐹)
61, 5nfcxfr 2748 1 𝑥recs(𝐹)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2737   E cep 4936  Oncon0 5625  wrecscwrecs 7270  recscrecs 7331
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ral 2900  df-rex 2901  df-rab 2904  df-v 3174  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-uni 4367  df-br 4578  df-opab 4638  df-xp 5033  df-cnv 5035  df-dm 5037  df-rn 5038  df-res 5039  df-ima 5040  df-pred 5582  df-iota 5753  df-fv 5797  df-wrecs 7271  df-recs 7332
This theorem is referenced by:  nfrdg  7374  nfoi  8279  aomclem8  36432
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