Metamath Proof Explorer


Theorem vcrel

Description: The class of all complex vector spaces is a relation. (Contributed by NM, 17-Mar-2007) (New usage is discouraged.)

Ref Expression
Assertion vcrel
|- Rel CVecOLD

Proof

Step Hyp Ref Expression
1 df-vc
 |-  CVecOLD = { <. g , s >. | ( g e. AbelOp /\ s : ( CC X. ran g ) --> ran g /\ A. x e. ran g ( ( 1 s x ) = x /\ A. y e. CC ( A. z e. ran g ( y s ( x g z ) ) = ( ( y s x ) g ( y s z ) ) /\ A. z e. CC ( ( ( y + z ) s x ) = ( ( y s x ) g ( z s x ) ) /\ ( ( y x. z ) s x ) = ( y s ( z s x ) ) ) ) ) ) }
2 1 relopabiv
 |-  Rel CVecOLD