Metamath Proof Explorer

Theorem finresfin

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

Proof

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