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Theorem nfiota 5772
 Description: Bound-variable hypothesis builder for the ℩ class. (Contributed by NM, 23-Aug-2011.)
Hypothesis
Ref Expression
nfiota.1 𝑥𝜑
Assertion
Ref Expression
nfiota 𝑥(℩𝑦𝜑)

Proof of Theorem nfiota
StepHypRef Expression
1 nftru 1721 . . 3 𝑦
2 nfiota.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfiotad 5771 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54trud 1484 1 𝑥(℩𝑦𝜑)
 Colors of variables: wff setvar class Syntax hints:  ⊤wtru 1476  Ⅎwnf 1699  Ⅎwnfc 2738  ℩cio 5766 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-sn 4126  df-uni 4373  df-iota 5768 This theorem is referenced by:  csbiota  5797  nffv  6110  nfsum1  14268  nfsum  14269  nfcprod1  14479  nfcprod  14480
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