Theorem elexi 2584

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 2583	. 2 ⊢ (𝐴 ∈ 𝐵 → 𝐴 ∈ V)
3	1, 2	ax-mp 7	1 ⊢ 𝐴 ∈ V

Syntax hints:   ∈ wcel 1409  Vcvv 2574

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038

This theorem depends on definitions:  df-bi 114  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576

This theorem is referenced by:  onunisuci  4196  ordsoexmid  4313  fnoei  6062  oeiexg  6063  endisj  6328  indpi  6497  prarloclemarch2  6574  prarloclemlt  6648  opelreal  6961  elreal  6962  elreal2  6964  eqresr  6969  c0ex  7078  1ex  7079  2ex  8061  3ex  8065  pnfex  8793  elxr  8796