Definition df-case 6977

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 6975. 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 6976	. 2 class case ( R , S )
4		cinl 6938	. . . . 5 class inl
5	4	ccnv 4546	. . . 4 class `'inl
6	1, 5	ccom 4551	. . 3 class ( R o. `'inl )
7		cinr 6939	. . . . 5 class inr
8	7	ccnv 4546	. . . 4 class `'inr
9	2, 8	ccom 4551	. . 3 class ( S o. `'inr )
10	6, 9	cun 3074	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1332	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  6978  casedm  6979  caserel  6980  caseinj  6982  caseinl  6984  caseinr  6985