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Theorem nfiotaxy 4899
 Description: Bound-variable hypothesis builder for the ℩ class. (Contributed by NM, 23-Aug-2011.)
Hypothesis
Ref Expression
nfiota.1 𝑥𝜑
Assertion
Ref Expression
nfiotaxy 𝑥(℩𝑦𝜑)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfiotaxy
StepHypRef Expression
1 nftru 1371 . . 3 𝑦
2 nfiota.1 . . . 4 𝑥𝜑
32a1i 9 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfiotadxy 4898 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54trud 1268 1 𝑥(℩𝑦𝜑)
 Colors of variables: wff set class Syntax hints:  ⊤wtru 1260  Ⅎwnf 1365  Ⅎwnfc 2181  ℩cio 4893 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-sn 3409  df-uni 3609  df-iota 4895 This theorem is referenced by:  csbiotag  4923  nffv  5213  nfsum1  10106  nfsum  10107
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