Metamath Proof Explorer


Theorem cardidg

Description: Any set is equinumerous to its cardinal number. Closed theorem form of cardid . (Contributed by David Moews, 1-May-2017)

Ref Expression
Assertion cardidg ABcardAA

Proof

Step Hyp Ref Expression
1 elex ABAV
2 cardeqv domcard=V
3 2 eleq2i AdomcardAV
4 cardid2 AdomcardcardAA
5 3 4 sylbir AVcardAA
6 1 5 syl ABcardAA