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Theorem bj-issetiv 32057
 Description: Version of bj-isseti 32058 with a dv condition on 𝑥, 𝑉. This proof uses only df-ex 1696, ax-gen 1713, ax-4 1728 and df-clel 2606 on top of propositional calculus. Prefer its use over bj-isseti 32058 when sufficient (in particular when 𝑉 is substituted for V). (Contributed by BJ, 14-Sep-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-issetiv.1 𝐴𝑉
Assertion
Ref Expression
bj-issetiv 𝑥 𝑥 = 𝐴
Distinct variable groups:   𝑥,𝐴   𝑥,𝑉

Proof of Theorem bj-issetiv
StepHypRef Expression
1 bj-issetiv.1 . 2 𝐴𝑉
2 bj-elissetv 32055 . 2 (𝐴𝑉 → ∃𝑥 𝑥 = 𝐴)
31, 2ax-mp 5 1 𝑥 𝑥 = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ∃wex 1695   ∈ wcel 1977 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728 This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-clel 2606 This theorem is referenced by:  bj-rexcom4bv  32065  bj-vtoclf  32100
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