Definition df-case 7282

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 7280. 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 7281	. 2 class case ( R , S )
4		cinl 7243	. . . . 5 class inl
5	4	ccnv 4724	. . . 4 class `'inl
6	1, 5	ccom 4729	. . 3 class ( R o. `'inl )
7		cinr 7244	. . . . 5 class inr
8	7	ccnv 4724	. . . 4 class `'inr
9	2, 8	ccom 4729	. . 3 class ( S o. `'inr )
10	6, 9	cun 3198	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1397	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  7283  casedm  7284  caserel  7285  caseinj  7287  caseinl  7289  caseinr  7290