Theorem ficardid

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

	Ref	Expression
Assertion	ficardid	$$⊢A\in \mathrm{Fin}\to \mathrm{card}\left(A\right)\approx A$$

Proof

Step	Hyp	Ref	Expression
1		finnum	$$⊢A\in \mathrm{Fin}\to A\in \mathrm{dom}\mathrm{card}$$
2		cardid2	$$⊢A\in \mathrm{dom}\mathrm{card}\to \mathrm{card}\left(A\right)\approx A$$
3	1 2	syl	$$⊢A\in \mathrm{Fin}\to \mathrm{card}\left(A\right)\approx A$$