Definition df-case 7262

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 7260. 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 7261	. 2 class case ( R , S )
4		cinl 7223	. . . . 5 class inl
5	4	ccnv 4718	. . . 4 class `'inl
6	1, 5	ccom 4723	. . 3 class ( R o. `'inl )
7		cinr 7224	. . . . 5 class inr
8	7	ccnv 4718	. . . 4 class `'inr
9	2, 8	ccom 4723	. . 3 class ( S o. `'inr )
10	6, 9	cun 3195	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1395	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  7263  casedm  7264  caserel  7265  caseinj  7267  caseinl  7269  caseinr  7270