Theorem elexd 2621

Description: If a class is a member of another class, it is a set. (Contributed by Glauco Siliprandi, 11-Oct-2020.)

Hypothesis

Ref	Expression
elexd.1	|- ( ph -> A e. V )

Assertion

Ref	Expression
elexd	|- ( ph -> A e. _V )

Proof of Theorem elexd

Step	Hyp	Ref	Expression
1		elexd.1	. 2 |- ( ph -> A e. V )
2		elex 2619	. 2 |- ( A e. V -> A e. _V )
3	1, 2	syl 14	1 |- ( ph -> A e. _V )

Syntax hints:   -> wi 4   e. wcel 1434   _Vcvv 2610

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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-v 2612

This theorem is referenced by:  tfr1onlemsucfn  6009  tfrcllemsucfn  6022  frecrdg  6077  unsnfidcel  6465  fnfi  6478  hashennn  9856  lcmval  10652  hashdvds  10804