Definition df-case 7083

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 7081. 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 7082	. 2 class case ( R , S )
4		cinl 7044	. . . . 5 class inl
5	4	ccnv 4626	. . . 4 class `'inl
6	1, 5	ccom 4631	. . 3 class ( R o. `'inl )
7		cinr 7045	. . . . 5 class inr
8	7	ccnv 4626	. . . 4 class `'inr
9	2, 8	ccom 4631	. . 3 class ( S o. `'inr )
10	6, 9	cun 3128	. 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  7084  casedm  7085  caserel  7086  caseinj  7088  caseinl  7090  caseinr  7091