Definition df-case 7375

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 7373. 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 7374	. 2 class case ( R , S )
4		cinl 7336	. . . . 5 class inl
5	4	ccnv 4748	. . . 4 class `'inl
6	1, 5	ccom 4753	. . 3 class ( R o. `'inl )
7		cinr 7337	. . . . 5 class inr
8	7	ccnv 4748	. . . 4 class `'inr
9	2, 8	ccom 4753	. . 3 class ( S o. `'inr )
10	6, 9	cun 3209	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1398	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  7376  casedm  7377  caserel  7378  caseinj  7380  caseinl  7382  caseinr  7383