Theorem nfriota1 7369

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 7362	. 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfiota1 6486	. 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	nfcxfr 2896	1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑)

Syntax hints:   ∧ wa 395   ∈ wcel 2108  Ⅎwnfc 2883  ℩cio 6482  ℩crio 7361

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 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2707

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 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-nfc 2885  df-ral 3052  df-rex 3061  df-v 3461  df-ss 3943  df-sn 4602  df-uni 4884  df-iota 6484  df-riota 7362

This theorem is referenced by:  riotaprop  7389  riotass2  7392  riotass  7393  riotaxfrd  7396  ttrcltr  9730  lble  12194  riotaneg  12221  zriotaneg  12706  nosupbnd1  27678  nosupbnd2  27680  noinfbnd1  27693  noinfbnd2  27695  poimirlem26  37670  riotaocN  39227  ltrniotaval  40600  cdlemksv2  40866  cdlemkuv2  40886  cdlemk36  40932  disjinfi  45216