Theorem issetiOLD 3506

Description: Obsolete version of isseti 3505 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

Step	Hyp	Ref	Expression
1		isseti.1	. 2 ⊢ 𝐴 ∈ V
2		isset 3503	. 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
3	1, 2	mpbi 232	1 ⊢ ∃𝑥 𝑥 = 𝐴

Syntax hints:   = wceq 1536  ∃wex 1779   ∈ wcel 2113  Vcvv 3491

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-ext 2792

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1780  df-sb 2069  df-clab 2799  df-cleq 2813  df-clel 2892  df-v 3493

This theorem is referenced by: (None)