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Theorem elissetOLD 3502
 Description: Obsolete version of elisset 3492 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 (𝐴𝑉 → ∃𝑥 𝑥 = 𝐴)
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝑉(𝑥)

Proof of Theorem elissetOLD
StepHypRef Expression
1 elex 3499 . 2 (𝐴𝑉𝐴 ∈ V)
2 isset 3493 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2sylib 221 1 (𝐴𝑉 → ∃𝑥 𝑥 = 𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538  ∃wex 1781   ∈ wcel 2115  Vcvv 3481 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 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3483 This theorem is referenced by: (None)
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