Metamath Proof Explorer

Theorem bnj1418

Description: Property of _pred . (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion bnj1418 
|- ( y e. _pred ( x , A , R ) -> y R x )

Proof

Step Hyp Ref Expression
1 breq1 
 |-  ( z = y -> ( z R x <-> y R x ) )
2 df-bnj14 
 |-  _pred ( x , A , R ) = { z e. A | z R x }
3 2 bnj1538 
 |-  ( z e. _pred ( x , A , R ) -> z R x )
4 1 3 vtoclga 
 |-  ( y e. _pred ( x , A , R ) -> y R x )