Description: Define the set of theorems. (Contributed by Mario Carneiro, 14-Jul-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | df-mthm | ⊢ mThm = ( 𝑡 ∈ V ↦ ( ◡ ( mStRed ‘ 𝑡 ) “ ( ( mStRed ‘ 𝑡 ) “ ( mPPSt ‘ 𝑡 ) ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | cmthm | ⊢ mThm | |
1 | vt | ⊢ 𝑡 | |
2 | cvv | ⊢ V | |
3 | cmsr | ⊢ mStRed | |
4 | 1 | cv | ⊢ 𝑡 |
5 | 4 3 | cfv | ⊢ ( mStRed ‘ 𝑡 ) |
6 | 5 | ccnv | ⊢ ◡ ( mStRed ‘ 𝑡 ) |
7 | cmpps | ⊢ mPPSt | |
8 | 4 7 | cfv | ⊢ ( mPPSt ‘ 𝑡 ) |
9 | 5 8 | cima | ⊢ ( ( mStRed ‘ 𝑡 ) “ ( mPPSt ‘ 𝑡 ) ) |
10 | 6 9 | cima | ⊢ ( ◡ ( mStRed ‘ 𝑡 ) “ ( ( mStRed ‘ 𝑡 ) “ ( mPPSt ‘ 𝑡 ) ) ) |
11 | 1 2 10 | cmpt | ⊢ ( 𝑡 ∈ V ↦ ( ◡ ( mStRed ‘ 𝑡 ) “ ( ( mStRed ‘ 𝑡 ) “ ( mPPSt ‘ 𝑡 ) ) ) ) |
12 | 0 11 | wceq | ⊢ mThm = ( 𝑡 ∈ V ↦ ( ◡ ( mStRed ‘ 𝑡 ) “ ( ( mStRed ‘ 𝑡 ) “ ( mPPSt ‘ 𝑡 ) ) ) ) |