Theorem qsex 8788

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

Step	Hyp	Ref	Expression
1		qsex.1	. 2 ⊢ 𝐴 ∈ V
2		qsexg 8787	. 2 ⊢ (𝐴 ∈ V → (𝐴 / 𝑅) ∈ V)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 / 𝑅) ∈ V

Syntax hints:   ∈ wcel 2099  Vcvv 3470   / cqs 8717

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-rep 5279

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-mo 2530  df-clab 2706  df-cleq 2720  df-clel 2806  df-rex 3067  df-v 3472  df-qs 8724

This theorem is referenced by:  prjspval  42021