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Theorem nfrecs 8414
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 8410 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
2 nfcv 2903 . . 3 𝑥 E
3 nfcv 2903 . . 3 𝑥On
4 nfrecs.f . . 3 𝑥𝐹
52, 3, 4nfwrecs 8340 . 2 𝑥wrecs( E , On, 𝐹)
61, 5nfcxfr 2901 1 𝑥recs(𝐹)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2888   E cep 5588  Oncon0 6386  wrecscwrecs 8335  recscrecs 8409
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-opab 5211  df-xp 5695  df-cnv 5697  df-co 5698  df-dm 5699  df-rn 5700  df-res 5701  df-ima 5702  df-pred 6323  df-iota 6516  df-fv 6571  df-ov 7434  df-frecs 8305  df-wrecs 8336  df-recs 8410
This theorem is referenced by:  nfrdg  8453  nfoi  9552  aomclem8  43050
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