Metamath Proof Explorer


Theorem bnj519

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Revised by Mario Carneiro, 6-May-2015) (New usage is discouraged.)

Ref Expression
Hypothesis bnj519.1
|- A e. _V
Assertion bnj519
|- ( B e. _V -> Fun { <. A , B >. } )

Proof

Step Hyp Ref Expression
1 bnj519.1
 |-  A e. _V
2 funsng
 |-  ( ( A e. _V /\ B e. _V ) -> Fun { <. A , B >. } )
3 1 2 mpan
 |-  ( B e. _V -> Fun { <. A , B >. } )