Theorem nfriota1 7373

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 7366	. 2 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfiota1 6486	. 2 ⊢ Ⅎ𝑥(℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	nfcxfr 2920	1 ⊢ Ⅎ𝑥(℩𝑥 ∈ 𝐴 𝜑)

This proof depends on syntax axioms:   ∧ wa 401   ∈ wcel 2145  Ⅎwnfc 2907  ℩cio 6482  ℩crio 7365

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-10 2178  ax-11 2194  ax-12 2213  ax-ext 2732

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 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-nfc 2909  df-ral 3077  df-rex 3087  df-v 3452  df-ss 3916  df-sn 4585  df-uni 4868  df-iota 6484  df-riota 7366

This theorem is used by:  riotaprop  7393  riotass2  7396  riotass  7397  riotaxfrd  7400  ttrcltr  9695  lble  12224  riotaneg  12251  zriotaneg  12767  nosupbnd1  27990  nosupbnd2  27992  noinfbnd1  28005  noinfbnd2  28007  poimirlem26  38478  riotaocN  40180  ltrniotaval  41552  cdlemksv2  41818  cdlemkuv2  41838  cdlemk36  41884  disjinfi  46122