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Definition df-mvl 33045
 Description: Define the set of valuations. (Contributed by Mario Carneiro, 14-Jul-2016.)
Assertion
Ref Expression
df-mvl mVL = (𝑡 ∈ V ↦ X𝑣 ∈ (mVR‘𝑡)((mUV‘𝑡) “ {((mType‘𝑡)‘𝑣)}))
Distinct variable group:   𝑣,𝑡

Detailed syntax breakdown of Definition df-mvl
StepHypRef Expression
1 cmvl 33032 . 2 class mVL
2 vt . . 3 setvar 𝑡
3 cvv 3442 . . 3 class V
4 vv . . . 4 setvar 𝑣
52cv 1537 . . . . 5 class 𝑡
6 cmvar 32887 . . . . 5 class mVR
75, 6cfv 6332 . . . 4 class (mVR‘𝑡)
8 cmuv 33031 . . . . . 6 class mUV
95, 8cfv 6332 . . . . 5 class (mUV‘𝑡)
104cv 1537 . . . . . . 7 class 𝑣
11 cmty 32888 . . . . . . . 8 class mType
125, 11cfv 6332 . . . . . . 7 class (mType‘𝑡)
1310, 12cfv 6332 . . . . . 6 class ((mType‘𝑡)‘𝑣)
1413csn 4528 . . . . 5 class {((mType‘𝑡)‘𝑣)}
159, 14cima 5526 . . . 4 class ((mUV‘𝑡) “ {((mType‘𝑡)‘𝑣)})
164, 7, 15cixp 8462 . . 3 class X𝑣 ∈ (mVR‘𝑡)((mUV‘𝑡) “ {((mType‘𝑡)‘𝑣)})
172, 3, 16cmpt 5114 . 2 class (𝑡 ∈ V ↦ X𝑣 ∈ (mVR‘𝑡)((mUV‘𝑡) “ {((mType‘𝑡)‘𝑣)}))
181, 17wceq 1538 1 wff mVL = (𝑡 ∈ V ↦ X𝑣 ∈ (mVR‘𝑡)((mUV‘𝑡) “ {((mType‘𝑡)‘𝑣)}))
 Colors of variables: wff setvar class This definition is referenced by: (None)
 Copyright terms: Public domain W3C validator