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Theorem bj-isseti 35345
Description: Version of isseti 3460 with a class variable 𝑉 in the hypothesis 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-isseti 35345 on special properties of the universal class V is obvious). Use bj-issetiv 35344 instead when sufficient (in particular when 𝑉 is substituted for V). (Contributed by BJ, 13-Jun-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-isseti.1 𝐴𝑉
Assertion
Ref Expression
bj-isseti 𝑥 𝑥 = 𝐴
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝑉(𝑥)

Proof of Theorem bj-isseti
StepHypRef Expression
1 bj-isseti.1 . 2 𝐴𝑉
2 elisset 2819 . 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-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-clel 2814
This theorem is referenced by:  bj-rexcom4b  35350
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