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Theorem qsex 8817
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 8816 . 2 (𝐴 ∈ V → (𝐴 / 𝑅) ∈ V)
31, 2ax-mp 5 1 (𝐴 / 𝑅) ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3479   / cqs 8745
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-rep 5278
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-mo 2539  df-clab 2714  df-cleq 2728  df-clel 2815  df-rex 3070  df-v 3481  df-qs 8752
This theorem is referenced by:  prjspval  42618
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