Metamath Proof Explorer


Definition df-msta

Description: Define the set of all statements. (Contributed by Mario Carneiro, 14-Jul-2016)

Ref Expression
Assertion df-msta mStat = ( 𝑡 ∈ V ↦ ran ( mStRed ‘ 𝑡 ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cmsta ⊢ mStat
1 vt ⊢ 𝑡
2 cvv ⊢ V
3 cmsr ⊢ mStRed
4 1 cv ⊢ 𝑡
5 4 3 cfv ⊢ ( mStRed ‘ 𝑡 )
6 5 crn ⊢ ran ( mStRed ‘ 𝑡 )
7 1 2 6 cmpt ⊢ ( 𝑡 ∈ V ↦ ran ( mStRed ‘ 𝑡 ) )
8 0 7 wceq ⊢ mStat = ( 𝑡 ∈ V ↦ ran ( mStRed ‘ 𝑡 ) )