Definition df-case 6831

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. 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 6830	. 2 class case ( R , S )
4		cinl 6793	. . . . 5 class inl
5	4	ccnv 4453	. . . 4 class `'inl
6	1, 5	ccom 4458	. . 3 class ( R o. `'inl )
7		cinr 6794	. . . . 5 class inr
8	7	ccnv 4453	. . . 4 class `'inr
9	2, 8	ccom 4458	. . 3 class ( S o. `'inr )
10	6, 9	cun 3000	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1290	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  6832  casedm  6833  caserel  6834  caseinj  6836  caseinl  6838