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

Theorem issetiOLD 3486
 Description: Obsolete version of isseti 3485 as of 28-Aug-2023. A way to say "𝐴 is a set" (inference form). (Contributed by NM, 24-Jun-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
isseti.1 𝐴 ∈ V
Assertion
Ref Expression
issetiOLD 𝑥 𝑥 = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem issetiOLD
StepHypRef Expression
1 isseti.1 . 2 𝐴 ∈ V
2 isset 3483 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbi 233 1 𝑥 𝑥 = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538  ∃wex 1781   ∈ wcel 2115  Vcvv 3471 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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2793 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071  df-clab 2800  df-cleq 2814  df-clel 2892  df-v 3473 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator