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Metamath Proof Explorer

Theorem fnssresd

Description: Restriction of a function to a subclass of its domain. (Contributed by Glauco Siliprandi, 5-Feb-2022)

Ref Expression
Hypotheses fnssresd.1 ⊢ φ → F Fn A
fnssresd.2 ⊢ φ → B ⊆ A
Assertion fnssresd ⊢ φ → F ↾ B Fn B

Proof

Step Hyp Ref Expression
1 fnssresd.1 ⊢ φ → F Fn A
2 fnssresd.2 ⊢ φ → B ⊆ A
3 fnssres ⊢ F Fn A ∧ B ⊆ A → F ↾ B Fn B
4 1 2 3 syl2anc ⊢ φ → F ↾ B Fn B