Definition df-case 7207

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 7205. 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 7206	. 2 class case ( R , S )
4		cinl 7168	. . . . 5 class inl
5	4	ccnv 4687	. . . 4 class `'inl
6	1, 5	ccom 4692	. . 3 class ( R o. `'inl )
7		cinr 7169	. . . . 5 class inr
8	7	ccnv 4687	. . . 4 class `'inr
9	2, 8	ccom 4692	. . 3 class ( S o. `'inr )
10	6, 9	cun 3168	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1373	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  7208  casedm  7209  caserel  7210  caseinj  7212  caseinl  7214  caseinr  7215