Definition df-dju 7015

Description: Disjoint union of two classes. This is a way of creating a class which contains elements corresponding to each element of 𝐴 or 𝐵, tagging each one with whether it came from 𝐴 or 𝐵. (Contributed by Jim Kingdon, 20-Jun-2022.)

Assertion

Ref	Expression
df-dju	⊢ (𝐴 ⊔ 𝐵) = (({∅} × 𝐴) ∪ ({1o} × 𝐵))

Detailed syntax breakdown of Definition df-dju

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cB	. . 3 class 𝐵
3	1, 2	cdju 7014	. 2 class (𝐴 ⊔ 𝐵)
4		c0 3414	. . . . 5 class ∅
5	4	csn 3583	. . . 4 class {∅}
6	5, 1	cxp 4609	. . 3 class ({∅} × 𝐴)
7		c1o 6388	. . . . 5 class 1o
8	7	csn 3583	. . . 4 class {1o}
9	8, 2	cxp 4609	. . 3 class ({1o} × 𝐵)
10	6, 9	cun 3119	. 2 class (({∅} × 𝐴) ∪ ({1o} × 𝐵))
11	3, 10	wceq 1348	1 wff (𝐴 ⊔ 𝐵) = (({∅} × 𝐴) ∪ ({1o} × 𝐵))

This definition is referenced by:  djueq12  7016  nfdju  7019  djuex  7020  djuexb  7021  djulclr  7026  djurclr  7027  djulcl  7028  djurcl  7029  djulclb  7032  djuunr  7043  eldju2ndl  7049  eldju2ndr  7050  xp2dju  7192  djucomen  7193  djuassen  7194  xpdjuen  7195  djulclALT  13836  djurclALT  13837