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Theorem isseti 2746
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 2744 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbi 145 1 𝑥 𝑥 = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1353  wex 1492  wcel 2148  Vcvv 2738
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-v 2740
This theorem is referenced by:  rexcom4b  2763  ceqsex  2776  vtoclf  2791  vtocl2  2793  vtocl3  2794  vtoclef  2811  eqvinc  2861  euind  2925  opabm  4281  eusv2nf  4457  dtruex  4559  limom  4614  isarep2  5304  dfoprab2  5922  rnoprab  5958  dmaddpq  7378  dmmulpq  7379  bj-inf2vnlem1  14725
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