Theorem ficardid

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

	Ref	Expression
Assertion	ficardid	⊢ ( 𝐴 ∈ Fin → ( card ‘ 𝐴 ) ≈ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		finnum	⊢ ( 𝐴 ∈ Fin → 𝐴 ∈ dom card )
2		cardid2	⊢ ( 𝐴 ∈ dom card → ( card ‘ 𝐴 ) ≈ 𝐴 )
3	1 2	syl	⊢ ( 𝐴 ∈ Fin → ( card ‘ 𝐴 ) ≈ 𝐴 )