Theorem nfrecs 7358

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 7355	. 2 ⊢ recs(𝐹) = wrecs( E , On, 𝐹)
2		nfcv 2751	. . 3 ⊢ Ⅎ𝑥 E
3		nfcv 2751	. . 3 ⊢ Ⅎ𝑥On
4		nfrecs.f	. . 3 ⊢ Ⅎ𝑥𝐹
5	2, 3, 4	nfwrecs 7296	. 2 ⊢ Ⅎ𝑥wrecs( E , On, 𝐹)
6	1, 5	nfcxfr 2749	1 ⊢ Ⅎ𝑥recs(𝐹)

Syntax hints:  Ⅎwnfc 2738   E cep 4947  Oncon0 5640  wrecscwrecs 7293  recscrecs 7354

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-opab 4644  df-xp 5044  df-cnv 5046  df-dm 5048  df-rn 5049  df-res 5050  df-ima 5051  df-pred 5597  df-iota 5768  df-fv 5812  df-wrecs 7294  df-recs 7355

This theorem is referenced by:  nfrdg  7397  nfoi  8302  aomclem8  36649