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

Theorem nfiota 6078
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 1886 . . 3 𝑦
2 nfiota.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfiotad 6077 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54mptru 1645 1 𝑥(℩𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wtru 1638  wnf 1863  wnfc 2946  cio 6072
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2069  ax-7 2105  ax-9 2166  ax-10 2186  ax-11 2202  ax-12 2215  ax-13 2422  ax-ext 2795
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2062  df-clab 2804  df-cleq 2810  df-clel 2813  df-nfc 2948  df-ral 3112  df-rex 3113  df-sn 4382  df-uni 4642  df-iota 6074
This theorem is referenced by:  csbiota  6104  nffv  6428  nfsum1  14663  nfsum  14664  nfcprod1  14881  nfcprod  14882  nfafv2  41825
  Copyright terms: Public domain W3C validator