Theorem elexi 2611

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 2610	. 2 ⊢ (𝐴 ∈ 𝐵 → 𝐴 ∈ V)
3	1, 2	ax-mp 7	1 ⊢ 𝐴 ∈ V

Syntax hints:   ∈ wcel 1433  Vcvv 2601

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603

This theorem is referenced by:  onunisuci  4187  ordsoexmid  4305  fnoei  6055  oeiexg  6056  endisj  6321  pm54.43  6459  indpi  6532  prarloclemarch2  6609  prarloclemlt  6683  opelreal  6996  elreal  6997  elreal2  6999  eqresr  7004  c0ex  7113  1ex  7114  2ex  8111  3ex  8115  pnfex  8847  elxr  8850