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Theorem isseti 2745
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 2743 . 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 2737
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 2739
This theorem is referenced by:  rexcom4b  2762  ceqsex  2775  vtoclf  2790  vtocl2  2792  vtocl3  2793  vtoclef  2810  eqvinc  2860  euind  2924  opabm  4280  eusv2nf  4456  dtruex  4558  limom  4613  isarep2  5303  dfoprab2  5921  rnoprab  5957  dmaddpq  7377  dmmulpq  7378  bj-inf2vnlem1  14692
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