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Theorem qsex 8815
Description: A quotient set exists. (Contributed by NM, 14-Aug-1995.)
Hypothesis
Ref Expression
qsex.1 𝐴 ∈ V
Assertion
Ref Expression
qsex (𝐴 / 𝑅) ∈ V

Proof of Theorem qsex
StepHypRef Expression
1 qsex.1 . 2 𝐴 ∈ V
2 qsexg 8814 . 2 (𝐴 ∈ V → (𝐴 / 𝑅) ∈ V)
31, 2ax-mp 5 1 (𝐴 / 𝑅) ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2106  Vcvv 3478   / cqs 8743
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-rep 5285
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-mo 2538  df-clab 2713  df-cleq 2727  df-clel 2814  df-rex 3069  df-v 3480  df-qs 8750
This theorem is referenced by:  prjspval  42590
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