Metamath Proof Explorer


Definition df-m0s

Description: Define a function mapping expressions to statements. (Contributed by Mario Carneiro, 14-Jul-2016)

Ref Expression
Assertion df-m0s m0St = ( 𝑎 ∈ V ↦ ⟨ ∅ , ∅ , 𝑎 ⟩ )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cm0s ⊢ m0St
1 va ⊢ 𝑎
2 cvv ⊢ V
3 c0 ⊢ ∅
4 1 cv ⊢ 𝑎
5 3 3 4 cotp ⊢ ⟨ ∅ , ∅ , 𝑎 ⟩
6 1 2 5 cmpt ⊢ ( 𝑎 ∈ V ↦ ⟨ ∅ , ∅ , 𝑎 ⟩ )
7 0 6 wceq ⊢ m0St = ( 𝑎 ∈ V ↦ ⟨ ∅ , ∅ , 𝑎 ⟩ )