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 ) ) ) ) |