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Theorem issetri 3509
Description: A way to say "𝐴 is a set" (inference form). (Contributed by NM, 21-Jun-1993.)
Hypothesis
Ref Expression
issetri.1 𝑥 𝑥 = 𝐴
Assertion
Ref Expression
issetri 𝐴 ∈ V
Distinct variable group:   𝑥,𝐴

Proof of Theorem issetri
StepHypRef Expression
1 issetri.1 . 2 𝑥 𝑥 = 𝐴
2 isset 3505 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbir 233 1 𝐴 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1530  wex 1773  wcel 2107  Vcvv 3493
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-ext 2791
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1774  df-sb 2063  df-clab 2798  df-cleq 2812  df-clel 2891  df-v 3495
This theorem is referenced by:  zfrep4  5191  0ex  5202  inex1  5212  vpwex  5269  zfpair2  5321  vuniex  7457  bj-snsetex  34263
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