Metamath Proof Explorer


Theorem harcl

Description: Values of the Hartogs function are ordinals (closure of the Hartogs function in the ordinals). (Contributed by Stefan O'Rear, 11-Feb-2015)

Ref Expression
Assertion harcl
|- ( har ` X ) e. On

Proof

Step Hyp Ref Expression
1 harf
 |-  har : _V --> On
2 0elon
 |-  (/) e. On
3 1 2 f0cli
 |-  ( har ` X ) e. On