Theorem nfriota1 7404

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 7397	. 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfiota1 6511	. 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	nfcxfr 2924	1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑)

This proof depends on syntax axioms:   ∧ wa 401   ∈ wcel 2147  Ⅎwnfc 2911  ℩cio 6507  ℩crio 7396

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-10 2180  ax-11 2197  ax-12 2216  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-nf 1817  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-nfc 2913  df-ral 3081  df-rex 3091  df-v 3456  df-ss 3901  df-sn 4589  df-uni 4871  df-iota 6509  df-riota 7397

This theorem is used by:  riotaprop  7424  riotass2  7427  riotass  7428  riotaxfrd  7431  ttrcltr  9741  lble  12293  riotaneg  12320  zriotaneg  12836  nosupbnd1  28098  nosupbnd2  28100  noinfbnd1  28113  noinfbnd2  28115  poimirlem26  38755  riotaocN  40457  ltrniotaval  41829  cdlemksv2  42095  cdlemkuv2  42115  cdlemk36  42161  disjinfi  46410