Theorem enfii

Description: A set equinumerous to a finite set is finite. (Contributed by Mario Carneiro, 12-Mar-2015)

	Ref	Expression
Assertion	enfii	⊢ ( ( 𝐵 ∈ Fin ∧ 𝐴 ≈ 𝐵 ) → 𝐴 ∈ Fin )

Proof

Step	Hyp	Ref	Expression
1		enfi	⊢ ( 𝐴 ≈ 𝐵 → ( 𝐴 ∈ Fin ↔ 𝐵 ∈ Fin ) )
2	1	biimparc	⊢ ( ( 𝐵 ∈ Fin ∧ 𝐴 ≈ 𝐵 ) → 𝐴 ∈ Fin )