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Theorem nfiotaxy 4871
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 1355 . . 3 𝑦
2 nfiota.1 . . . 4 𝑥𝜑
32a1i 9 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfiotadxy 4870 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54trud 1252 1 𝑥(℩𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  wtru 1244  wnf 1349  wnfc 2165  cio 4865
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-sn 3381  df-uni 3581  df-iota 4867
This theorem is referenced by:  csbiotag  4895  nffv  5185  nfsum1  9875  nfsum  9876
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