Description: The restriction of a finite set is finite. (Contributed by Alexander van der Vekens, 3-Jan-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | finresfin | ⊢ ( 𝐸 ∈ Fin → ( 𝐸 ↾ 𝐵 ) ∈ Fin ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resss | ⊢ ( 𝐸 ↾ 𝐵 ) ⊆ 𝐸 | |
2 | ssfi | ⊢ ( ( 𝐸 ∈ Fin ∧ ( 𝐸 ↾ 𝐵 ) ⊆ 𝐸 ) → ( 𝐸 ↾ 𝐵 ) ∈ Fin ) | |
3 | 1 2 | mpan2 | ⊢ ( 𝐸 ∈ Fin → ( 𝐸 ↾ 𝐵 ) ∈ Fin ) |