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Theorem issetri 3350
Description: A way to say "𝐴 is a set" (inference rule). (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 3347 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbir 221 1 𝐴 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1632  wex 1853  wcel 2139  Vcvv 3340
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-12 2196  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1635  df-ex 1854  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-v 3342
This theorem is referenced by:  zfrep4  4931  0ex  4942  inex1  4951  pwex  4997  zfpair2  5056  uniex  7119  bj-snsetex  33275
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