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Theorem nfriota 5401
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(y A φ)
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)   A(x,y)

Proof of Theorem nfriota
StepHypRef Expression
1 nftru 1335 . . 3 y
2 nfriota.1 . . . 4 xφ
32a1i 9 . . 3 ( ⊤ → Ⅎxφ)
4 nfriota.2 . . . 4 xA
54a1i 9 . . 3 ( ⊤ → xA)
61, 3, 5nfriotadxy 5400 . 2 ( ⊤ → x(y A φ))
76trud 1237 1 x(y A φ)
Colors of variables: wff set class
Syntax hints:  wtru 1229  wnf 1329  wnfc 2147  crio 5392
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-sn 3356  df-uni 3555  df-iota 4794  df-riota 5393
This theorem is referenced by:  csbriotag  5404
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