MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfiota Structured version   Visualization version   GIF version

Theorem nfiota 5893
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 1770 . . 3 𝑦
2 nfiota.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfiotad 5892 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54trud 1533 1 𝑥(℩𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wtru 1524  wnf 1748  wnfc 2780  cio 5887
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-rex 2947  df-sn 4211  df-uni 4469  df-iota 5889
This theorem is referenced by:  csbiota  5919  nffv  6236  nfsum1  14464  nfsum  14465  nfcprod1  14684  nfcprod  14685
  Copyright terms: Public domain W3C validator