Metamath Proof Explorer

Theorem vcex

Description: The components of a complex vector space are sets. (Contributed by NM, 31-May-2008) (New usage is discouraged.)

Ref Expression
Assertion vcex 
|- ( <. G , S >. e. CVecOLD -> ( G e. _V /\ S e. _V ) )

Proof

Step Hyp Ref Expression
1 df-br 
 |-  ( G CVecOLD S <-> <. G , S >. e. CVecOLD )
2 vcrel 
 |-  Rel CVecOLD
3 2 brrelex12i 
 |-  ( G CVecOLD S -> ( G e. _V /\ S e. _V ) )
4 1 3 sylbir 
 |-  ( <. G , S >. e. CVecOLD -> ( G e. _V /\ S e. _V ) )