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Theorem bj-issetiv 35344
Description: Version of bj-isseti 35345 with a disjoint variable condition on 𝑥, 𝑉. The hypothesis uses 𝑉 instead of V for extra generality. This is indeed more general than isseti 3460 as long as elex 3463 is not available (and the non-dependence of bj-issetiv 35344 on special properties of the universal class V is obvious). Prefer its use over bj-isseti 35345 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 elissetv 2818 . 2 (𝐴𝑉 → ∃𝑥 𝑥 = 𝐴)
31, 2ax-mp 5 1 𝑥 𝑥 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  wex 1781  wcel 2106
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 1913  ax-6 1971  ax-7 2011  ax-8 2108
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1782  df-clel 2814
This theorem is referenced by:  bj-rexcom4bv  35349  bj-vtoclf  35382
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