Metamath Proof Explorer


Theorem funmpt2

Description: Functionality of a class given by a maps-to notation. (Contributed by FL, 17-Feb-2008) (Revised by Mario Carneiro, 31-May-2014)

Ref Expression
Hypothesis funmpt2.1
|- F = ( x e. A |-> B )
Assertion funmpt2
|- Fun F

Proof

Step Hyp Ref Expression
1 funmpt2.1
 |-  F = ( x e. A |-> B )
2 funmpt
 |-  Fun ( x e. A |-> B )
3 1 funeqi
 |-  ( Fun F <-> Fun ( x e. A |-> B ) )
4 2 3 mpbir
 |-  Fun F