Definition df-case 7045

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 7043. 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 7044	. 2 class case ( R , S )
4		cinl 7006	. . . . 5 class inl
5	4	ccnv 4602	. . . 4 class `'inl
6	1, 5	ccom 4607	. . 3 class ( R o. `'inl )
7		cinr 7007	. . . . 5 class inr
8	7	ccnv 4602	. . . 4 class `'inr
9	2, 8	ccom 4607	. . 3 class ( S o. `'inr )
10	6, 9	cun 3113	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1343	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  7046  casedm  7047  caserel  7048  caseinj  7050  caseinl  7052  caseinr  7053