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Metamath Proof Explorer

Theorem fcod

Description: Composition of two mappings. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypotheses fcod.1 ⊢ φ → F : B ⟶ C
fcod.2 ⊢ φ → G : A ⟶ B
Assertion fcod ⊢ φ → F ∘ G : A ⟶ C

Proof

Step Hyp Ref Expression
1 fcod.1 ⊢ φ → F : B ⟶ C
2 fcod.2 ⊢ φ → G : A ⟶ B
3 fco ⊢ F : B ⟶ C ∧ G : A ⟶ B → F ∘ G : A ⟶ C
4 1 2 3 syl2anc ⊢ φ → F ∘ G : A ⟶ C