Theorem elissetOLD 3512

Description: Obsolete version of elisset 3502 as of 28-Aug-2023. An element of a class exists. (Contributed by NM, 1-May-1995.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
elissetOLD	⊢ (𝐴 ∈ 𝑉 → ∃𝑥 𝑥 = 𝐴)

Distinct variable group:   𝑥,𝐴

Allowed substitution hint:   𝑉(𝑥)

Proof of Theorem elissetOLD

Step	Hyp	Ref	Expression
1		elex 3509	. 2 ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ V)
2		isset 3503	. 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
3	1, 2	sylib 220	1 ⊢ (𝐴 ∈ 𝑉 → ∃𝑥 𝑥 = 𝐴)

Syntax hints:   → wi 4   = 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)