Definition df-case 7326

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 7324. 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 7325	. 2 class case ( R , S )
4		cinl 7287	. . . . 5 class inl
5	4	ccnv 4730	. . . 4 class `'inl
6	1, 5	ccom 4735	. . 3 class ( R o. `'inl )
7		cinr 7288	. . . . 5 class inr
8	7	ccnv 4730	. . . 4 class `'inr
9	2, 8	ccom 4735	. . 3 class ( S o. `'inr )
10	6, 9	cun 3199	. 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  7327  casedm  7328  caserel  7329  caseinj  7331  caseinl  7333  caseinr  7334