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Definition df-case 6937
Description: The "case" construction: if 𝐹:𝐴𝑋 and 𝐺:𝐵𝑋 are functions, then case(𝐹, 𝐺):(𝐴𝐵)⟶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 6935. 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) = ((𝑅inl) ∪ (𝑆inr))

Detailed syntax breakdown of Definition df-case
StepHypRef Expression
1 cR . . 3 class 𝑅
2 cS . . 3 class 𝑆
31, 2cdjucase 6936 . 2 class case(𝑅, 𝑆)
4 cinl 6898 . . . . 5 class inl
54ccnv 4508 . . . 4 class inl
61, 5ccom 4513 . . 3 class (𝑅inl)
7 cinr 6899 . . . . 5 class inr
87ccnv 4508 . . . 4 class inr
92, 8ccom 4513 . . 3 class (𝑆inr)
106, 9cun 3039 . 2 class ((𝑅inl) ∪ (𝑆inr))
113, 10wceq 1316 1 wff case(𝑅, 𝑆) = ((𝑅inl) ∪ (𝑆inr))
Colors of variables: wff set class
This definition is referenced by:  casefun  6938  casedm  6939  caserel  6940  caseinj  6942  caseinl  6944  caseinr  6945
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