Metamath Proof Explorer


Theorem elex

Description: If a class is a member of another class, then it is a set. Theorem 6.12 of Quine p. 44. (Contributed by NM, 26-May-1993) (Proof shortened by Andrew Salmon, 8-Jun-2011) (Proof shortened by Wolf Lammen, 28-May-2025)

Ref Expression
Assertion elex A B A V

Proof

Step Hyp Ref Expression
1 elissetv A B x x = A
2 isset A V x x = A
3 1 2 sylibr A B A V