Definition df-bj-sethom 33078

Description: Define the set of functions (morphisms of sets) between two sets. Same as df-map 7859 with arguments swapped. TODO: prove the same staple lemmas as for ↑_𝑚.

Remark: one may define Set⟶ = (𝑥 ∈ (1^st Struct ) , y e. ( 1st Struct ) ↦ {𝑓 ∣ 𝑓:(Base x ) --> ( Base 𝑦)}) so that for morphisms between other structures, one could write ... {𝑓 ∈ (𝑥 Set⟶ 𝑦) ∣...

(Contributed by BJ, 11-Apr-2020.)

Assertion

Ref	Expression
df-bj-sethom	⊢ Set⟶ = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑥⟶𝑦})

Distinct variable group:   𝑥,𝑓,𝑦

Detailed syntax breakdown of Definition df-bj-sethom

Step	Hyp	Ref	Expression
1		csethom 33075	. 2 class Set⟶
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cvv 3200	. . 3 class V
5	2	cv 1482	. . . . 5 class 𝑥
6	3	cv 1482	. . . . 5 class 𝑦
7		vf	. . . . . 6 setvar 𝑓
8	7	cv 1482	. . . . 5 class 𝑓
9	5, 6, 8	wf 5884	. . . 4 wff 𝑓:𝑥⟶𝑦
10	9, 7	cab 2608	. . 3 class {𝑓 ∣ 𝑓:𝑥⟶𝑦}
11	2, 3, 4, 4, 10	cmpt2 6652	. 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑥⟶𝑦})
12	1, 11	wceq 1483	1 wff Set⟶ = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑥⟶𝑦})

This definition is referenced by: (None)