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Mathbox for Mario Carneiro |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-mdv | Structured version Visualization version GIF version |
Description: Define the set of distinct variable conditions, which are pairs of distinct variables. (Contributed by Mario Carneiro, 14-Jul-2016.) |
Ref | Expression |
---|---|
df-mdv | ⊢ mDV = (𝑡 ∈ V ↦ (((mVR‘𝑡) × (mVR‘𝑡)) ∖ I )) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmdv 30619 | . 2 class mDV | |
2 | vt | . . 3 setvar 𝑡 | |
3 | cvv 3173 | . . 3 class V | |
4 | 2 | cv 1474 | . . . . . 6 class 𝑡 |
5 | cmvar 30612 | . . . . . 6 class mVR | |
6 | 4, 5 | cfv 5804 | . . . . 5 class (mVR‘𝑡) |
7 | 6, 6 | cxp 5036 | . . . 4 class ((mVR‘𝑡) × (mVR‘𝑡)) |
8 | cid 4948 | . . . 4 class I | |
9 | 7, 8 | cdif 3537 | . . 3 class (((mVR‘𝑡) × (mVR‘𝑡)) ∖ I ) |
10 | 2, 3, 9 | cmpt 4643 | . 2 class (𝑡 ∈ V ↦ (((mVR‘𝑡) × (mVR‘𝑡)) ∖ I )) |
11 | 1, 10 | wceq 1475 | 1 wff mDV = (𝑡 ∈ V ↦ (((mVR‘𝑡) × (mVR‘𝑡)) ∖ I )) |
Colors of variables: wff setvar class |
This definition is referenced by: mdvval 30655 |
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