MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfrecs Structured version   Visualization version   GIF version

Theorem nfrecs 8396
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 8392 . 2 recs(𝐹) = wrecs( E , On, 𝐹)
2 nfcv 2899 . . 3 𝑥 E
3 nfcv 2899 . . 3 𝑥On
4 nfrecs.f . . 3 𝑥𝐹
52, 3, 4nfwrecs 8322 . 2 𝑥wrecs( E , On, 𝐹)
61, 5nfcxfr 2897 1 𝑥recs(𝐹)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2879   E cep 5581  Oncon0 6369  wrecscwrecs 8317  recscrecs 8391
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-nfc 2881  df-ral 3059  df-rex 3068  df-rab 3430  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-uni 4909  df-br 5149  df-opab 5211  df-xp 5684  df-cnv 5686  df-co 5687  df-dm 5688  df-rn 5689  df-res 5690  df-ima 5691  df-pred 6305  df-iota 6500  df-fv 6556  df-ov 7423  df-frecs 8287  df-wrecs 8318  df-recs 8392
This theorem is referenced by:  nfrdg  8435  nfoi  9538  aomclem8  42485
  Copyright terms: Public domain W3C validator