Metamath Proof Explorer


Definition df-mthm

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 ) ) ) )

Detailed syntax breakdown

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 ) ) ) )