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Theorem issetri 3457
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 3454 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbir 230 1 𝐴 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wex 1780  wcel 2105  Vcvv 3441
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3443
This theorem is referenced by:  zfrep4  5240  0ex  5251  inex1  5261  vpwex  5320  zfpair2  5373  vuniex  7654  bj-snsetex  35247
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