Theorem nfrecs 8362

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 8359	. 2 ⊢ recs(𝐹) = wrecs( E , On, 𝐹)
2		nfcv 2925	. . 3 ⊢ Ⅎ𝑥 E
3		nfcv 2925	. . 3 ⊢ Ⅎ𝑥On
4		nfrecs.f	. . 3 ⊢ Ⅎ𝑥𝐹
5	2, 3, 4	nfwrecs 8312	. 2 ⊢ Ⅎ𝑥wrecs( E , On, 𝐹)
6	1, 5	nfcxfr 2923	1 ⊢ Ⅎ𝑥recs(𝐹)

Syntax hints:  Ⅎwnfc 2910   E cep 5562  Oncon0 6362  wrecscwrecs 8309  recscrecs 8358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-10 2176  ax-11 2192  ax-12 2213  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-nf 1814  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-nfc 2912  df-ral 3080  df-rex 3090  df-rab 3417  df-v 3457  df-dif 3909  df-un 3911  df-in 3913  df-ss 3923  df-nul 4288  df-if 4489  df-sn 4591  df-pr 4593  df-op 4597  df-uni 4874  df-br 5111  df-opab 5175  df-xp 5669  df-cnv 5671  df-co 5672  df-dm 5673  df-rn 5674  df-res 5675  df-ima 5676  df-pred 6304  df-iota 6494  df-fv 6546  df-ov 7415  df-frecs 8279  df-wrecs 8310  df-recs 8359

This theorem is referenced by:  nfrdg  8402  nfoi  9477  aomclem8  43771