Theorem elexi 2631

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 2630	. 2 ⊢ (𝐴 ∈ 𝐵 → 𝐴 ∈ V)
3	1, 2	ax-mp 7	1 ⊢ 𝐴 ∈ V

Syntax hints:   ∈ wcel 1438  Vcvv 2619

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 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-v 2621

This theorem is referenced by:  onunisuci  4250  ordsoexmid  4368  1oex  6171  fnoei  6195  oeiexg  6196  endisj  6520  unfiexmid  6608  snexxph  6638  djuex  6715  infnninf  6784  nnnninf  6785  pm54.43  6797  prarloclemarch2  6957  opelreal  7344  elreal  7345  elreal2  7347  eqresr  7352  c0ex  7461  1ex  7462  pnfex  7520  2ex  8465  3ex  8469  elxr  9216  0nninf  11539  nninfex  11547