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Definition df-case 7077
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 7075. 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 7076 . 2  class case ( R ,  S )
4 cinl 7038 . . . . 5  class inl
54ccnv 4622 . . . 4  class  `'inl
61, 5ccom 4627 . . 3  class  ( R  o.  `'inl )
7 cinr 7039 . . . . 5  class inr
87ccnv 4622 . . . 4  class  `'inr
92, 8ccom 4627 . . 3  class  ( S  o.  `'inr )
106, 9cun 3127 . 2  class  ( ( R  o.  `'inl )  u.  ( S  o.  `'inr ) )
113, 10wceq 1353 1  wff case ( R ,  S )  =  ( ( R  o.  `'inl )  u.  ( S  o.  `'inr )
)
Colors of variables: wff set class
This definition is referenced by:  casefun  7078  casedm  7079  caserel  7080  caseinj  7082  caseinl  7084  caseinr  7085
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