Definition df-case 7414

Description: The "case" construction: if F : A --> X and G : B --> X are functions, then case ( F , G ) : ( A ⊔ B ) --> X is the natural function obtained by a definition by cases, hence the name. It is the unique function whose existence is asserted by the universal property of disjoint unions updjud 7412. The definition is adapted to make sense also for binary relations (where the universal property also holds). (Contributed by MC and BJ, 10-Jul-2022.)

Assertion

Ref	Expression
df-case	|- case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

Detailed syntax breakdown of Definition df-case

Step	Hyp	Ref	Expression
1		cR	. . 3 class R
2		cS	. . 3 class S
3	1, 2	cdjucase 7413	. 2 class case ( R , S )
4		cinl 7375	. . . . 5 class inl
5	4	ccnv 4768	. . . 4 class `'inl
6	1, 5	ccom 4773	. . 3 class ( R o. `'inl )
7		cinr 7376	. . . . 5 class inr
8	7	ccnv 4768	. . . 4 class `'inr
9	2, 8	ccom 4773	. . 3 class ( S o. `'inr )
10	6, 9	cun 3218	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1402	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  7415  casedm  7416  caserel  7417  caseinj  7419  caseinl  7421  caseinr  7422