Theorem nfriota1 7351

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 7344	. 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfiota1 6466	. 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	nfcxfr 2889	1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑)

Syntax hints:   ∧ wa 395   ∈ wcel 2109  Ⅎwnfc 2876  ℩cio 6462  ℩crio 7343

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 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-nfc 2878  df-ral 3045  df-rex 3054  df-v 3449  df-ss 3931  df-sn 4590  df-uni 4872  df-iota 6464  df-riota 7344

This theorem is referenced by:  riotaprop  7371  riotass2  7374  riotass  7375  riotaxfrd  7378  ttrcltr  9669  lble  12135  riotaneg  12162  zriotaneg  12647  nosupbnd1  27626  nosupbnd2  27628  noinfbnd1  27641  noinfbnd2  27643  poimirlem26  37640  riotaocN  39202  ltrniotaval  40575  cdlemksv2  40841  cdlemkuv2  40861  cdlemk36  40907  disjinfi  45186