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Metamath Proof Explorer

Theorem fvco3d

Description: Value of a function composition. Deduction form of fvco3 . (Contributed by Stanislas Polu, 9-Mar-2020)

Ref Expression
Hypotheses fvco3d.1 ⊢ φ → G : A ⟶ B
fvco3d.2 ⊢ φ → C ∈ A
Assertion fvco3d ⊢ φ → F ∘ G ⁡ C = F ⁡ G ⁡ C

Proof

Step Hyp Ref Expression
1 fvco3d.1 ⊢ φ → G : A ⟶ B
2 fvco3d.2 ⊢ φ → C ∈ A
3 fvco3 ⊢ G : A ⟶ B ∧ C ∈ A → F ∘ G ⁡ C = F ⁡ G ⁡ C
4 1 2 3 syl2anc ⊢ φ → F ∘ G ⁡ C = F ⁡ G ⁡ C