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Theorem isseti 2738
Description: A way to say "𝐴 is a set" (inference form). (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
isseti.1 𝐴 ∈ V
Assertion
Ref Expression
isseti 𝑥 𝑥 = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem isseti
StepHypRef Expression
1 isseti.1 . 2 𝐴 ∈ V
2 isset 2736 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbi 144 1 𝑥 𝑥 = 𝐴
Colors of variables: wff set class
Syntax hints:   = 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:  rexcom4b  2755  ceqsex  2768  vtoclf  2783  vtocl2  2785  vtocl3  2786  vtoclef  2803  eqvinc  2853  euind  2917  opabm  4265  eusv2nf  4441  dtruex  4543  limom  4598  isarep2  5285  dfoprab2  5900  rnoprab  5936  dmaddpq  7341  dmmulpq  7342  bj-inf2vnlem1  14005
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