Definition df-case 7186

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 7184. 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 7185	. 2 class case ( R , S )
4		cinl 7147	. . . . 5 class inl
5	4	ccnv 4674	. . . 4 class `'inl
6	1, 5	ccom 4679	. . 3 class ( R o. `'inl )
7		cinr 7148	. . . . 5 class inr
8	7	ccnv 4674	. . . 4 class `'inr
9	2, 8	ccom 4679	. . 3 class ( S o. `'inr )
10	6, 9	cun 3164	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1373	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  7187  casedm  7188  caserel  7189  caseinj  7191  caseinl  7193  caseinr  7194