Metamath Proof Explorer


Definition df-hf

Description: Define the hereditarily finite sets. These are the finite sets whose elements are finite, and so forth. (Contributed by Scott Fenton, 9-Jul-2015)

Ref Expression
Assertion df-hf
|- Hf = U. ( R1 " _om )

Detailed syntax breakdown

Step Hyp Ref Expression
0 chf
 |-  Hf
1 cr1
 |-  R1
2 com
 |-  _om
3 1 2 cima
 |-  ( R1 " _om )
4 3 cuni
 |-  U. ( R1 " _om )
5 0 4 wceq
 |-  Hf = U. ( R1 " _om )