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Definition df-mpps 31673
Description: Define the set of provable pre-statements. (Contributed by Mario Carneiro, 14-Jul-2016.)
Assertion
Ref Expression
df-mpps mPPSt = (𝑡 ∈ V ↦ {⟨⟨𝑑, ⟩, 𝑎⟩ ∣ (⟨𝑑, , 𝑎⟩ ∈ (mPreSt‘𝑡) ∧ 𝑎 ∈ (𝑑(mCls‘𝑡)))})
Distinct variable group:   𝑎,𝑑,,𝑡

Detailed syntax breakdown of Definition df-mpps
StepHypRef Expression
1 cmpps 31653 . 2 class mPPSt
2 vt . . 3 setvar 𝑡
3 cvv 3328 . . 3 class V
4 vd . . . . . . . 8 setvar 𝑑
54cv 1619 . . . . . . 7 class 𝑑
6 vh . . . . . . . 8 setvar
76cv 1619 . . . . . . 7 class
8 va . . . . . . . 8 setvar 𝑎
98cv 1619 . . . . . . 7 class 𝑎
105, 7, 9cotp 4317 . . . . . 6 class 𝑑, , 𝑎
112cv 1619 . . . . . . 7 class 𝑡
12 cmpst 31648 . . . . . . 7 class mPreSt
1311, 12cfv 6037 . . . . . 6 class (mPreSt‘𝑡)
1410, 13wcel 2127 . . . . 5 wff 𝑑, , 𝑎⟩ ∈ (mPreSt‘𝑡)
15 cmcls 31652 . . . . . . . 8 class mCls
1611, 15cfv 6037 . . . . . . 7 class (mCls‘𝑡)
175, 7, 16co 6801 . . . . . 6 class (𝑑(mCls‘𝑡))
189, 17wcel 2127 . . . . 5 wff 𝑎 ∈ (𝑑(mCls‘𝑡))
1914, 18wa 383 . . . 4 wff (⟨𝑑, , 𝑎⟩ ∈ (mPreSt‘𝑡) ∧ 𝑎 ∈ (𝑑(mCls‘𝑡)))
2019, 4, 6, 8coprab 6802 . . 3 class {⟨⟨𝑑, ⟩, 𝑎⟩ ∣ (⟨𝑑, , 𝑎⟩ ∈ (mPreSt‘𝑡) ∧ 𝑎 ∈ (𝑑(mCls‘𝑡)))}
212, 3, 20cmpt 4869 . 2 class (𝑡 ∈ V ↦ {⟨⟨𝑑, ⟩, 𝑎⟩ ∣ (⟨𝑑, , 𝑎⟩ ∈ (mPreSt‘𝑡) ∧ 𝑎 ∈ (𝑑(mCls‘𝑡)))})
221, 21wceq 1620 1 wff mPPSt = (𝑡 ∈ V ↦ {⟨⟨𝑑, ⟩, 𝑎⟩ ∣ (⟨𝑑, , 𝑎⟩ ∈ (mPreSt‘𝑡) ∧ 𝑎 ∈ (𝑑(mCls‘𝑡)))})
Colors of variables: wff setvar class
This definition is referenced by:  mppsval  31747
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