Definition df-mvl 33581

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

Step	Hyp	Ref	Expression
1		cmvl 33568	. 2 class mVL
2		vt	. . 3 setvar 𝑡
3		cvv 3432	. . 3 class V
4		vv	. . . 4 setvar 𝑣
5	2	cv 1538	. . . . 5 class 𝑡
6		cmvar 33423	. . . . 5 class mVR
7	5, 6	cfv 6433	. . . 4 class (mVR‘𝑡)
8		cmuv 33567	. . . . . 6 class mUV
9	5, 8	cfv 6433	. . . . 5 class (mUV‘𝑡)
10	4	cv 1538	. . . . . . 7 class 𝑣
11		cmty 33424	. . . . . . . 8 class mType
12	5, 11	cfv 6433	. . . . . . 7 class (mType‘𝑡)
13	10, 12	cfv 6433	. . . . . 6 class ((mType‘𝑡)‘𝑣)
14	13	csn 4561	. . . . 5 class {((mType‘𝑡)‘𝑣)}
15	9, 14	cima 5592	. . . 4 class ((mUV‘𝑡) “ {((mType‘𝑡)‘𝑣)})
16	4, 7, 15	cixp 8685	. . 3 class X𝑣 ∈ (mVR‘𝑡)((mUV‘𝑡) “ {((mType‘𝑡)‘𝑣)})
17	2, 3, 16	cmpt 5157	. 2 class (𝑡 ∈ V ↦ X𝑣 ∈ (mVR‘𝑡)((mUV‘𝑡) “ {((mType‘𝑡)‘𝑣)}))
18	1, 17	wceq 1539	1 wff mVL = (𝑡 ∈ V ↦ X𝑣 ∈ (mVR‘𝑡)((mUV‘𝑡) “ {((mType‘𝑡)‘𝑣)}))

This definition is referenced by: (None)