Metamath Proof Explorer


Definition df-rel

Description: Define the relation predicate. Definition 6.4(1) of TakeutiZaring p. 23. For alternate definitions, see dfrel2 and dfrel3 . (Contributed by NM, 1-Aug-1994)

Ref Expression
Assertion df-rel
|- ( Rel A <-> A C_ ( _V X. _V ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA
 |-  A
1 0 wrel
 |-  Rel A
2 cvv
 |-  _V
3 2 2 cxp
 |-  ( _V X. _V )
4 0 3 wss
 |-  A C_ ( _V X. _V )
5 1 4 wb
 |-  ( Rel A <-> A C_ ( _V X. _V ) )