Metamath Proof Explorer

Theorem euhash1

Description: The size of a set is 1 in terms of existential uniqueness. (Contributed by Alexander van der Vekens, 8-Feb-2018)

Ref Expression
Assertion euhash1 
|- ( V e. W -> ( ( # ` V ) = 1 <-> E! a a e. V ) )

Proof

Step Hyp Ref Expression
1 hashen1 
 |-  ( V e. W -> ( ( # ` V ) = 1 <-> V ~~ 1o ) )
2 euen1b 
 |-  ( V ~~ 1o <-> E! a a e. V )
3 1 2 bitrdi 
 |-  ( V e. W -> ( ( # ` V ) = 1 <-> E! a a e. V ) )