Theorem nfrecs 8416

Description: Bound-variable hypothesis builder for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.)

Hypothesis

Ref	Expression
nfrecs.f	⊢ Ⅎ𝑥𝐹

Assertion

Ref	Expression
nfrecs	⊢ Ⅎ𝑥recs(𝐹)

Proof of Theorem nfrecs

Step	Hyp	Ref	Expression
1		df-recs 8412	. 2 ⊢ recs(𝐹) = wrecs( E , On, 𝐹)
2		nfcv 2904	. . 3 ⊢ Ⅎ𝑥 E
3		nfcv 2904	. . 3 ⊢ Ⅎ𝑥On
4		nfrecs.f	. . 3 ⊢ Ⅎ𝑥𝐹
5	2, 3, 4	nfwrecs 8342	. 2 ⊢ Ⅎ𝑥wrecs( E , On, 𝐹)
6	1, 5	nfcxfr 2902	1 ⊢ Ⅎ𝑥recs(𝐹)

Syntax hints:  Ⅎwnfc 2889   E cep 5582  Oncon0 6383  wrecscwrecs 8337  recscrecs 8411

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-10 2140  ax-11 2156  ax-12 2176  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-nf 1783  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-nfc 2891  df-ral 3061  df-rex 3070  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-in 3957  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4626  df-pr 4628  df-op 4632  df-uni 4907  df-br 5143  df-opab 5205  df-xp 5690  df-cnv 5692  df-co 5693  df-dm 5694  df-rn 5695  df-res 5696  df-ima 5697  df-pred 6320  df-iota 6513  df-fv 6568  df-ov 7435  df-frecs 8307  df-wrecs 8338  df-recs 8412

This theorem is referenced by:  nfrdg  8455  nfoi  9555  aomclem8  43078