Theorem nfrecs 8014

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 8011	. 2 ⊢ recs(𝐹) = wrecs( E , On, 𝐹)
2		nfcv 2980	. . 3 ⊢ Ⅎ𝑥 E
3		nfcv 2980	. . 3 ⊢ Ⅎ𝑥On
4		nfrecs.f	. . 3 ⊢ Ⅎ𝑥𝐹
5	2, 3, 4	nfwrecs 7952	. 2 ⊢ Ⅎ𝑥wrecs( E , On, 𝐹)
6	1, 5	nfcxfr 2978	1 ⊢ Ⅎ𝑥recs(𝐹)

Syntax hints:  Ⅎwnfc 2964   E cep 5467  Oncon0 6194  wrecscwrecs 7949  recscrecs 8010

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-ral 3146  df-rex 3147  df-rab 3150  df-v 3499  df-dif 3942  df-un 3944  df-in 3946  df-ss 3955  df-nul 4295  df-if 4471  df-sn 4571  df-pr 4573  df-op 4577  df-uni 4842  df-br 5070  df-opab 5132  df-xp 5564  df-cnv 5566  df-dm 5568  df-rn 5569  df-res 5570  df-ima 5571  df-pred 6151  df-iota 6317  df-fv 6366  df-wrecs 7950  df-recs 8011

This theorem is referenced by:  nfrdg  8053  nfoi  8981  aomclem8  39667