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 ) |
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 ) |