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

Theorem nfabg 2926
 Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 2379. See nfab 2925 for a version with more disjoint variable conditions, but not requiring ax-13 2379. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.)
Hypothesis
Ref Expression
nfabg.1 𝑥𝜑
Assertion
Ref Expression
nfabg 𝑥{𝑦𝜑}

Proof of Theorem nfabg
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 nfabg.1 . . 3 𝑥𝜑
21nfsabg 2749 . 2 𝑥 𝑧 ∈ {𝑦𝜑}
32nfci 2902 1 𝑥{𝑦𝜑}
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnf 1785  {cab 2735  Ⅎwnfc 2899 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-11 2158  ax-12 2175  ax-13 2379 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2736  df-nfc 2901 This theorem is referenced by:  nfaba1g  2928  nfiung  4915  nfiing  4916
 Copyright terms: Public domain W3C validator