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Metamath Proof Explorer

Theorem fnssres

Description: Restriction of a function with a subclass of its domain. (Contributed by NM, 2-Aug-1994)

Ref Expression
Assertion fnssres ⊢ F Fn A ∧ B ⊆ A → F ↾ B Fn B

Proof

Step Hyp Ref Expression
1 fnssresb ⊢ F Fn A → F ↾ B Fn B ↔ B ⊆ A
2 1 biimpar ⊢ F Fn A ∧ B ⊆ A → F ↾ B Fn B