Theorem nfriota1 7367

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 7360	. 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfiota1 6494	. 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	nfcxfr 2902	1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑)

Syntax hints:   ∧ wa 397   ∈ wcel 2107  Ⅎwnfc 2884  ℩cio 6490  ℩crio 7359

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-ral 3063  df-rex 3072  df-v 3477  df-in 3954  df-ss 3964  df-sn 4628  df-uni 4908  df-iota 6492  df-riota 7360

This theorem is referenced by:  riotaprop  7388  riotass2  7391  riotass  7392  riotaxfrd  7395  ttrcltr  9707  lble  12162  riotaneg  12189  zriotaneg  12671  nosupbnd1  27197  nosupbnd2  27199  noinfbnd1  27212  noinfbnd2  27214  poimirlem26  36452  riotaocN  38017  ltrniotaval  39390  cdlemksv2  39656  cdlemkuv2  39676  cdlemk36  39722  disjinfi  43824