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Definition df-case 6962
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 6960. 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 6961 . 2  class case ( R ,  S )
4 cinl 6923 . . . . 5  class inl
54ccnv 4533 . . . 4  class  `'inl
61, 5ccom 4538 . . 3  class  ( R  o.  `'inl )
7 cinr 6924 . . . . 5  class inr
87ccnv 4533 . . . 4  class  `'inr
92, 8ccom 4538 . . 3  class  ( S  o.  `'inr )
106, 9cun 3064 . 2  class  ( ( R  o.  `'inl )  u.  ( S  o.  `'inr ) )
113, 10wceq 1331 1  wff case ( R ,  S )  =  ( ( R  o.  `'inl )  u.  ( S  o.  `'inr )
)
Colors of variables: wff set class
This definition is referenced by:  casefun  6963  casedm  6964  caserel  6965  caseinj  6967  caseinl  6969  caseinr  6970
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