Theorem qsex 8746

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 8745	. 2 ⊢ (𝐴 ∈ V → (𝐴 / 𝑅) ∈ V)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 / 𝑅) ∈ V

Syntax hints:   ∈ wcel 2109  Vcvv 3447   / cqs 8670

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-rep 5234

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-mo 2533  df-clab 2708  df-cleq 2721  df-clel 2803  df-rex 3054  df-v 3449  df-qs 8677

This theorem is referenced by:  prjspval  42591