Theorem qsex 8775

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 8774	. 2 ⊢ (𝐴 ∈ V → (𝐴 / 𝑅) ∈ V)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 / 𝑅) ∈ V

This proof depends on syntax axioms:   ∈ wcel 2145  Vcvv 3453   / cqs 8698

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734  ax-rep 5236

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-mo 2566  df-clab 2741  df-cleq 2754  df-clel 2837  df-rex 3089  df-v 3455  df-qs 8705

This theorem is used by:  prjspval  43451