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Definition df-msa 33294
Description: Define the set of syntax axioms. (Contributed by Mario Carneiro, 14-Jul-2016.)
Assertion
Ref Expression
df-msa mSA = (𝑡 ∈ V ↦ {𝑎 ∈ (mEx‘𝑡) ∣ ((m0St‘𝑎) ∈ (mAx‘𝑡) ∧ (1st𝑎) ∈ (mVT‘𝑡) ∧ Fun ((2nd𝑎) ↾ (mVR‘𝑡)))})
Distinct variable group:   𝑡,𝑎

Detailed syntax breakdown of Definition df-msa
StepHypRef Expression
1 cmsa 33284 . 2 class mSA
2 vt . . 3 setvar 𝑡
3 cvv 3420 . . 3 class V
4 va . . . . . . . 8 setvar 𝑎
54cv 1542 . . . . . . 7 class 𝑎
6 cm0s 33283 . . . . . . 7 class m0St
75, 6cfv 6397 . . . . . 6 class (m0St‘𝑎)
82cv 1542 . . . . . . 7 class 𝑡
9 cmax 33163 . . . . . . 7 class mAx
108, 9cfv 6397 . . . . . 6 class (mAx‘𝑡)
117, 10wcel 2111 . . . . 5 wff (m0St‘𝑎) ∈ (mAx‘𝑡)
12 c1st 7777 . . . . . . 7 class 1st
135, 12cfv 6397 . . . . . 6 class (1st𝑎)
14 cmvt 33161 . . . . . . 7 class mVT
158, 14cfv 6397 . . . . . 6 class (mVT‘𝑡)
1613, 15wcel 2111 . . . . 5 wff (1st𝑎) ∈ (mVT‘𝑡)
17 c2nd 7778 . . . . . . . . 9 class 2nd
185, 17cfv 6397 . . . . . . . 8 class (2nd𝑎)
1918ccnv 5564 . . . . . . 7 class (2nd𝑎)
20 cmvar 33159 . . . . . . . 8 class mVR
218, 20cfv 6397 . . . . . . 7 class (mVR‘𝑡)
2219, 21cres 5567 . . . . . 6 class ((2nd𝑎) ↾ (mVR‘𝑡))
2322wfun 6391 . . . . 5 wff Fun ((2nd𝑎) ↾ (mVR‘𝑡))
2411, 16, 23w3a 1089 . . . 4 wff ((m0St‘𝑎) ∈ (mAx‘𝑡) ∧ (1st𝑎) ∈ (mVT‘𝑡) ∧ Fun ((2nd𝑎) ↾ (mVR‘𝑡)))
25 cmex 33165 . . . . 5 class mEx
268, 25cfv 6397 . . . 4 class (mEx‘𝑡)
2724, 4, 26crab 3066 . . 3 class {𝑎 ∈ (mEx‘𝑡) ∣ ((m0St‘𝑎) ∈ (mAx‘𝑡) ∧ (1st𝑎) ∈ (mVT‘𝑡) ∧ Fun ((2nd𝑎) ↾ (mVR‘𝑡)))}
282, 3, 27cmpt 5149 . 2 class (𝑡 ∈ V ↦ {𝑎 ∈ (mEx‘𝑡) ∣ ((m0St‘𝑎) ∈ (mAx‘𝑡) ∧ (1st𝑎) ∈ (mVT‘𝑡) ∧ Fun ((2nd𝑎) ↾ (mVR‘𝑡)))})
291, 28wceq 1543 1 wff mSA = (𝑡 ∈ V ↦ {𝑎 ∈ (mEx‘𝑡) ∣ ((m0St‘𝑎) ∈ (mAx‘𝑡) ∧ (1st𝑎) ∈ (mVT‘𝑡) ∧ Fun ((2nd𝑎) ↾ (mVR‘𝑡)))})
Colors of variables: wff setvar class
This definition is referenced by: (None)
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