Definition df-case 7185

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 7183. 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 7184	. 2 class case ( R , S )
4		cinl 7146	. . . . 5 class inl
5	4	ccnv 4673	. . . 4 class `'inl
6	1, 5	ccom 4678	. . 3 class ( R o. `'inl )
7		cinr 7147	. . . . 5 class inr
8	7	ccnv 4673	. . . 4 class `'inr
9	2, 8	ccom 4678	. . 3 class ( S o. `'inr )
10	6, 9	cun 3163	. 2 class ( ( R o. `'inl ) u. ( S o. `'inr ) )
11	3, 10	wceq 1372	1 wff case ( R , S ) = ( ( R o. `'inl ) u. ( S o. `'inr ) )

This definition is referenced by:  casefun  7186  casedm  7187  caserel  7188  caseinj  7190  caseinl  7192  caseinr  7193