Theorem qsex 8767

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 8766	. 2 ⊢ (𝐴 ∈ V → (𝐴 / 𝑅) ∈ V)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 / 𝑅) ∈ V

Syntax hints:   ∈ wcel 2098  Vcvv 3466   / cqs 8699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-rep 5276

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-mo 2526  df-clab 2702  df-cleq 2716  df-clel 2802  df-rex 3063  df-v 3468  df-qs 8706

This theorem is referenced by:  prjspval  41859