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Definition df-case 6884
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 6882. 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 6883 . 2 class case(𝑅, 𝑆)
4 cinl 6845 . . . . 5 class inl
54ccnv 4476 . . . 4 class inl
61, 5ccom 4481 . . 3 class (𝑅inl)
7 cinr 6846 . . . . 5 class inr
87ccnv 4476 . . . 4 class inr
92, 8ccom 4481 . . 3 class (𝑆inr)
106, 9cun 3019 . 2 class ((𝑅inl) ∪ (𝑆inr))
113, 10wceq 1299 1 wff case(𝑅, 𝑆) = ((𝑅inl) ∪ (𝑆inr))
Colors of variables: wff set class
This definition is referenced by:  casefun  6885  casedm  6886  caserel  6887  caseinj  6889  caseinl  6891  caseinr  6892
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