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Theorem nfriota 5530
 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 1396 . . 3 𝑦
2 nfriota.1 . . . 4 𝑥𝜑
32a1i 9 . . 3 (⊤ → Ⅎ𝑥𝜑)
4 nfriota.2 . . . 4 𝑥𝐴
54a1i 9 . . 3 (⊤ → 𝑥𝐴)
61, 3, 5nfriotadxy 5529 . 2 (⊤ → 𝑥(𝑦𝐴 𝜑))
76trud 1294 1 𝑥(𝑦𝐴 𝜑)
 Colors of variables: wff set class Syntax hints:  ⊤wtru 1286  Ⅎwnf 1390  Ⅎwnfc 2210  ℩crio 5520 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rex 2359  df-sn 3423  df-uni 3623  df-iota 4918  df-riota 5521 This theorem is referenced by:  csbriotag  5533  lble  8169
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