Theorem qsexg

Description: A quotient set exists. (Contributed by FL, 19-May-2007) (Revised by Mario Carneiro, 9-Jul-2014)

	Ref	Expression
Assertion	qsexg	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 / 𝑅 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		df-qs	⊢ ( 𝐴 / 𝑅 ) = { 𝑦 ∣ ∃ 𝑥 ∈ 𝐴 𝑦 = [ 𝑥 ] 𝑅 }
2		abrexexg	⊢ ( 𝐴 ∈ 𝑉 → { 𝑦 ∣ ∃ 𝑥 ∈ 𝐴 𝑦 = [ 𝑥 ] 𝑅 } ∈ V )
3	1 2	eqeltrid	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 / 𝑅 ) ∈ V )