Theorem nfriota1 7362

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 7355	. 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfiota1 6481	. 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	nfcxfr 2924	1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑)

Syntax hints:   ∧ wa 399   ∈ wcel 2144  Ⅎwnfc 2911  ℩cio 6477  ℩crio 7354

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-10 2177  ax-11 2193  ax-12 2214  ax-ext 2736

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1565  df-ex 1802  df-nf 1806  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-nfc 2913  df-ral 3079  df-rex 3089  df-v 3458  df-ss 3923  df-sn 4585  df-uni 4868  df-iota 6479  df-riota 7355

This theorem is referenced by:  riotaprop  7382  riotass2  7385  riotass  7386  riotaxfrd  7389  ttrcltr  9673  lble  12146  riotaneg  12173  zriotaneg  12688  nosupbnd1  27780  nosupbnd2  27782  noinfbnd1  27795  noinfbnd2  27797  poimirlem26  38150  riotaocN  39838  ltrniotaval  41210  cdlemksv2  41476  cdlemkuv2  41496  cdlemk36  41542  disjinfi  45775