Definition df-case 7082

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 7080. 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 7081	. 2 class case ( R , S )
4		cinl 7043	. . . . 5 class inl
5	4	ccnv 4625	. . . 4 class `'inl
6	1, 5	ccom 4630	. . 3 class ( R o. `'inl )
7		cinr 7044	. . . . 5 class inr
8	7	ccnv 4625	. . . 4 class `'inr
9	2, 8	ccom 4630	. . 3 class ( S o. `'inr )
10	6, 9	cun 3127	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1353	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  7083  casedm  7084  caserel  7085  caseinj  7087  caseinl  7089  caseinr  7090