Metamath Proof Explorer
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 ) ) |