Theorem nfrecs 8311

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 8308	. 2 ⊢ recs(𝐹) = wrecs( E , On, 𝐹)
2		nfcv 2902	. . 3 ⊢ Ⅎ𝑥 E
3		nfcv 2902	. . 3 ⊢ Ⅎ𝑥On
4		nfrecs.f	. . 3 ⊢ Ⅎ𝑥𝐹
5	2, 3, 4	nfwrecs 8261	. 2 ⊢ Ⅎ𝑥wrecs( E , On, 𝐹)
6	1, 5	nfcxfr 2900	1 ⊢ Ⅎ𝑥recs(𝐹)

Syntax hints:  Ⅎwnfc 2887   E cep 5524  Oncon0 6317  wrecscwrecs 8258  recscrecs 8307

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-10 2152  ax-11 2168  ax-12 2189  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-nf 1791  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-nfc 2889  df-ral 3055  df-rex 3065  df-rab 3393  df-v 3434  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4269  df-if 4462  df-sn 4563  df-pr 4565  df-op 4569  df-uni 4846  df-br 5080  df-opab 5142  df-xp 5631  df-cnv 5633  df-co 5634  df-dm 5635  df-rn 5636  df-res 5637  df-ima 5638  df-pred 6259  df-iota 6448  df-fv 6500  df-ov 7366  df-frecs 8228  df-wrecs 8259  df-recs 8308

This theorem is referenced by:  nfrdg  8350  nfoi  9426  aomclem8  43513