Theorem nfriota1 7322

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 7315	. 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfiota1 6450	. 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	nfcxfr 2896	1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑)

Syntax hints:   ∧ wa 395   ∈ wcel 2113  Ⅎwnfc 2883  ℩cio 6446  ℩crio 7314

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-10 2146  ax-11 2162  ax-12 2184  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-nf 1785  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-nfc 2885  df-ral 3052  df-rex 3061  df-v 3442  df-ss 3918  df-sn 4581  df-uni 4864  df-iota 6448  df-riota 7315

This theorem is referenced by:  riotaprop  7342  riotass2  7345  riotass  7346  riotaxfrd  7349  ttrcltr  9625  lble  12094  riotaneg  12121  zriotaneg  12605  nosupbnd1  27682  nosupbnd2  27684  noinfbnd1  27697  noinfbnd2  27699  poimirlem26  37847  riotaocN  39469  ltrniotaval  40841  cdlemksv2  41107  cdlemkuv2  41127  cdlemk36  41173  disjinfi  45436