Metamath Proof Explorer


Theorem ficardid

Description: A finite set is equinumerous to its cardinal number. (Contributed by Mario Carneiro, 21-Sep-2013)

Ref Expression
Assertion ficardid
|- ( A e. Fin -> ( card ` A ) ~~ A )

Proof

Step Hyp Ref Expression
1 finnum
 |-  ( A e. Fin -> A e. dom card )
2 cardid2
 |-  ( A e. dom card -> ( card ` A ) ~~ A )
3 1 2 syl
 |-  ( A e. Fin -> ( card ` A ) ~~ A )