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Theorem nfriota 6848
Description: A variable not free in a wff remains so in a restricted iota descriptor. (Contributed by NM, 12-Oct-2011.)
Hypotheses
Ref Expression
nfriota.1 𝑥𝜑
nfriota.2 𝑥𝐴
Assertion
Ref Expression
nfriota 𝑥(𝑦𝐴 𝜑)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝐴(𝑥,𝑦)

Proof of Theorem nfriota
StepHypRef Expression
1 nftru 1900 . . 3 𝑦
2 nfriota.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
4 nfriota.2 . . . 4 𝑥𝐴
54a1i 11 . . 3 (⊤ → 𝑥𝐴)
61, 3, 5nfriotad 6847 . 2 (⊤ → 𝑥(𝑦𝐴 𝜑))
76mptru 1661 1 𝑥(𝑦𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wtru 1654  wnf 1879  wnfc 2928  crio 6838
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-ral 3094  df-rex 3095  df-sn 4369  df-uni 4629  df-iota 6064  df-riota 6839
This theorem is referenced by:  csbriota  6851  nfoi  8661  lble  11267  nosupbnd1  32373  riotasvd  34977  riotasv2d  34978  riotasv2s  34979  cdleme26ee  36381  cdleme31sn1  36402  cdlemefs32sn1aw  36435  cdleme43fsv1snlem  36441  cdleme41sn3a  36454  cdleme32d  36465  cdleme32f  36467  cdleme40m  36488  cdleme40n  36489  cdlemk36  36934  cdlemk38  36936  cdlemkid  36957  cdlemk19x  36964  cdlemk11t  36967
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