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Metamath Proof Explorer

Theorem efmndfv

Description: The function value of an endofunction. (Contributed by AV, 27-Jan-2024)

Ref Expression
Hypotheses efmndbas.g ⊢ G = EndoFMnd ⁡ A
efmndbas.b ⊢ B = Base G
Assertion efmndfv ⊢ F ∈ B ∧ X ∈ A → F ⁡ X ∈ A

Proof

Step Hyp Ref Expression
1 efmndbas.g ⊢ G = EndoFMnd ⁡ A
2 efmndbas.b ⊢ B = Base G
3 1 2 efmndbasf ⊢ F ∈ B → F : A ⟶ A
4 3 ffvelcdmda ⊢ F ∈ B ∧ X ∈ A → F ⁡ X ∈ A