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Theorem nfiota 5814
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 1727 . . 3 𝑦
2 nfiota.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfiotad 5813 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54trud 1490 1 𝑥(℩𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wtru 1481  wnf 1705  wnfc 2748  cio 5808
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2912  df-rex 2913  df-sn 4149  df-uni 4403  df-iota 5810
This theorem is referenced by:  csbiota  5840  nffv  6155  nfsum1  14354  nfsum  14355  nfcprod1  14565  nfcprod  14566
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