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Metamath Proof Explorer

Theorem 0func

Description: The functor from the empty category. (Contributed by Zhi Wang, 7-Oct-2025) (Proof shortened by Zhi Wang, 17-Oct-2025)

Ref Expression
Hypothesis 0func.c ⊢ φ → C ∈ Cat
Assertion 0func ⊢ φ → ∅ Func C = ∅ ∅

Proof

Step Hyp Ref Expression
1 0func.c ⊢ φ → C ∈ Cat
2 0ex ⊢ ∅ ∈ V
3 2 a1i ⊢ φ → ∅ ∈ V
4 base0 ⊢ ∅ = Base ∅
5 4 a1i ⊢ φ → ∅ = Base ∅
6 3 5 1 0funcg ⊢ φ → ∅ Func C = ∅ ∅