Theorem nfriota1 7378

Description: The abstraction variable in a restricted iota descriptor isn't free. (Contributed by NM, 12-Oct-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)

Assertion

Ref	Expression
nfriota1	⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑)

Distinct variable group:   𝑥,𝐴

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem nfriota1

Step	Hyp	Ref	Expression
1		df-riota 7371	. 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfiota1 6498	. 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	nfcxfr 2930	1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑)

Syntax hints:   ∧ wa 400   ∈ wcel 2150  Ⅎwnfc 2917  ℩cio 6494  ℩crio 7370

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2152  ax-9 2160  ax-10 2183  ax-11 2199  ax-12 2220  ax-ext 2742

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1571  df-ex 1808  df-nf 1812  df-sb 2099  df-clab 2749  df-cleq 2762  df-clel 2845  df-nfc 2919  df-ral 3087  df-rex 3097  df-v 3464  df-ss 3930  df-sn 4595  df-uni 4878  df-iota 6496  df-riota 7371

This theorem is referenced by:  riotaprop  7398  riotass2  7401  riotass  7402  riotaxfrd  7405  ttrcltr  9688  lble  12170  riotaneg  12197  zriotaneg  12712  nosupbnd1  27858  nosupbnd2  27860  noinfbnd1  27873  noinfbnd2  27875  poimirlem26  38245  riotaocN  39933  ltrniotaval  41305  cdlemksv2  41571  cdlemkuv2  41591  cdlemk36  41637  disjinfi  45862