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Definition df-case 6831
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. 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
StepHypRef Expression
1 cR . . 3  class  R
2 cS . . 3  class  S
31, 2cdjucase 6830 . 2  class case ( R ,  S )
4 cinl 6793 . . . . 5  class inl
54ccnv 4453 . . . 4  class  `'inl
61, 5ccom 4458 . . 3  class  ( R  o.  `'inl )
7 cinr 6794 . . . . 5  class inr
87ccnv 4453 . . . 4  class  `'inr
92, 8ccom 4458 . . 3  class  ( S  o.  `'inr )
106, 9cun 3000 . 2  class  ( ( R  o.  `'inl )  u.  ( S  o.  `'inr ) )
113, 10wceq 1290 1  wff case ( R ,  S )  =  ( ( R  o.  `'inl )  u.  ( S  o.  `'inr )
)
Colors of variables: wff set class
This definition is referenced by:  casefun  6832  casedm  6833  caserel  6834  caseinj  6836  caseinl  6838
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