Definition df-mvh 33354

Description: Define the mapping from variables to their variable hypothesis. (Contributed by Mario Carneiro, 14-Jul-2016.)

Assertion

Ref	Expression
df-mvh	⊢ mVH = (𝑡 ∈ V ↦ (𝑣 ∈ (mVR‘𝑡) ↦ ⟨((mType‘𝑡)‘𝑣), ⟨“𝑣”⟩⟩))

Distinct variable group:   𝑣,𝑡

Detailed syntax breakdown of Definition df-mvh

Step	Hyp	Ref	Expression
1		cmvh 33334	. 2 class mVH
2		vt	. . 3 setvar 𝑡
3		cvv 3422	. . 3 class V
4		vv	. . . 4 setvar 𝑣
5	2	cv 1538	. . . . 5 class 𝑡
6		cmvar 33323	. . . . 5 class mVR
7	5, 6	cfv 6418	. . . 4 class (mVR‘𝑡)
8	4	cv 1538	. . . . . 6 class 𝑣
9		cmty 33324	. . . . . . 7 class mType
10	5, 9	cfv 6418	. . . . . 6 class (mType‘𝑡)
11	8, 10	cfv 6418	. . . . 5 class ((mType‘𝑡)‘𝑣)
12	8	cs1 14228	. . . . 5 class ⟨“𝑣”⟩
13	11, 12	cop 4564	. . . 4 class ⟨((mType‘𝑡)‘𝑣), ⟨“𝑣”⟩⟩
14	4, 7, 13	cmpt 5153	. . 3 class (𝑣 ∈ (mVR‘𝑡) ↦ ⟨((mType‘𝑡)‘𝑣), ⟨“𝑣”⟩⟩)
15	2, 3, 14	cmpt 5153	. 2 class (𝑡 ∈ V ↦ (𝑣 ∈ (mVR‘𝑡) ↦ ⟨((mType‘𝑡)‘𝑣), ⟨“𝑣”⟩⟩))
16	1, 15	wceq 1539	1 wff mVH = (𝑡 ∈ V ↦ (𝑣 ∈ (mVR‘𝑡) ↦ ⟨((mType‘𝑡)‘𝑣), ⟨“𝑣”⟩⟩))

This definition is referenced by:  mvhfval  33395