Theorem elexi 2869

Description: If a class is a member of another class, it is a set. (Contributed by NM, 11-Jun-1994.)

Hypothesis

Ref	Expression
elisseti.1	⊢ A ∈ B

Assertion

Ref	Expression
elexi	⊢ A ∈ V

Proof of Theorem elexi

Step	Hyp	Ref	Expression
1		elisseti.1	. 2 ⊢ A ∈ B
2		elex 2868	. 2 ⊢ (A ∈ B → A ∈ V)
3	1, 2	ax-mp 5	1 ⊢ A ∈ V

Syntax hints:   ∈ wcel 1710  Vcvv 2860

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2862

This theorem is referenced by:  caovmo  5646  spacvallem1  6282  nchoicelem16  6305