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Theorem elisset 2744
Description: An element of a class exists. (Contributed by NM, 1-May-1995.)
Assertion
Ref Expression
elisset (𝐴𝑉 → ∃𝑥 𝑥 = 𝐴)
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝑉(𝑥)

Proof of Theorem elisset
StepHypRef Expression
1 elex 2741 . 2 (𝐴𝑉𝐴 ∈ V)
2 isset 2736 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2sylib 121 1 (𝐴𝑉 → ∃𝑥 𝑥 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1348  wex 1485  wcel 2141  Vcvv 2730
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-v 2732
This theorem is referenced by:  elex22  2745  elex2  2746  ceqsalt  2756  ceqsalg  2758  cgsexg  2765  cgsex2g  2766  cgsex4g  2767  vtoclgft  2780  vtocleg  2801  vtoclegft  2802  spc2egv  2820  spc2gv  2821  spc3egv  2822  spc3gv  2823  eqvincg  2854  tpid3g  3696  iinexgm  4138  copsex2t  4228  copsex2g  4229  ralxfr2d  4447  rexxfr2d  4448  fliftf  5775  eloprabga  5937  ovmpt4g  5972  spc2ed  6209  eroveu  6600  supelti  6975  genpassl  7473  genpassu  7474  eqord1  8389  nn1suc  8884  bj-inex  13902
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