Metamath Proof Explorer

Theorem structn0fun

Description: A structure without the empty set is a function. (Contributed by AV, 13-Nov-2021)

Ref Expression
Assertion structn0fun 
|- ( F Struct X -> Fun ( F \ { (/) } ) )

Proof

Step Hyp Ref Expression
1 isstruct2 
 |-  ( F Struct X <-> ( X e. ( <_ i^i ( NN X. NN ) ) /\ Fun ( F \ { (/) } ) /\ dom F C_ ( ... ` X ) ) )
2 1 simp2bi 
 |-  ( F Struct X -> Fun ( F \ { (/) } ) )