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Theorem nfrecs 8322
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 8318 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
2 nfcv 2904 . . 3 𝑥 E
3 nfcv 2904 . . 3 𝑥On
4 nfrecs.f . . 3 𝑥𝐹
52, 3, 4nfwrecs 8248 . 2 𝑥wrecs( E , On, 𝐹)
61, 5nfcxfr 2902 1 𝑥recs(𝐹)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2884   E cep 5537  Oncon0 6318  wrecscwrecs 8243  recscrecs 8317
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-ral 3062  df-rex 3071  df-rab 3407  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-uni 4867  df-br 5107  df-opab 5169  df-xp 5640  df-cnv 5642  df-co 5643  df-dm 5644  df-rn 5645  df-res 5646  df-ima 5647  df-pred 6254  df-iota 6449  df-fv 6505  df-ov 7361  df-frecs 8213  df-wrecs 8244  df-recs 8318
This theorem is referenced by:  nfrdg  8361  nfoi  9455  aomclem8  41431
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