Theorem qsex 8716

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 8715	. 2 ⊢ (𝐴 ∈ V → (𝐴 / 𝑅) ∈ V)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 / 𝑅) ∈ V

Syntax hints:   ∈ wcel 2119  Vcvv 3432   / cqs 8639

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712  ax-rep 5206

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-mo 2543  df-clab 2719  df-cleq 2732  df-clel 2815  df-rex 3065  df-v 3434  df-qs 8646

This theorem is referenced by:  prjspval  43054