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Mirrors > Home > MPE Home > Th. List > df-slot | Structured version Visualization version GIF version |
Description: Define slot extractor for posets and related structures. Note that the function argument can be any set, although it is meaningful only if it is a member of Poset (df-poset 16769) when used for posets or of Grp (df-grp 17248) when used from groups. (Contributed by Mario Carneiro, 22-Sep-2015.) |
Ref | Expression |
---|---|
df-slot | ⊢ Slot 𝐴 = (𝑥 ∈ V ↦ (𝑥‘𝐴)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | 1 | cslot 15694 | . 2 class Slot 𝐴 |
3 | vx | . . 3 setvar 𝑥 | |
4 | cvv 3173 | . . 3 class V | |
5 | 3 | cv 1474 | . . . 4 class 𝑥 |
6 | 1, 5 | cfv 5804 | . . 3 class (𝑥‘𝐴) |
7 | 3, 4, 6 | cmpt 4643 | . 2 class (𝑥 ∈ V ↦ (𝑥‘𝐴)) |
8 | 2, 7 | wceq 1475 | 1 wff Slot 𝐴 = (𝑥 ∈ V ↦ (𝑥‘𝐴)) |
Colors of variables: wff setvar class |
This definition is referenced by: slotfn 15709 strfvnd 15710 ndxid 15716 dfpleOLD 15789 |
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