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Theorem nfiota 6318
 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 1798 . . 3 𝑦
2 nfiota.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfiotad 6317 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54mptru 1537 1 𝑥(℩𝑦𝜑)
 Colors of variables: wff setvar class Syntax hints:  ⊤wtru 1531  Ⅎwnf 1777  Ⅎwnfc 2966  ℩cio 6310 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-13 2385  ax-ext 2798 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ral 3148  df-rex 3149  df-sn 4565  df-uni 4838  df-iota 6312 This theorem is referenced by:  nfsum  15038  nfafv2  43283
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