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Definition df-case 7117
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 7115. 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 7116 . 2 class case(𝑅, 𝑆)
4 cinl 7078 . . . . 5 class inl
54ccnv 4646 . . . 4 class inl
61, 5ccom 4651 . . 3 class (𝑅inl)
7 cinr 7079 . . . . 5 class inr
87ccnv 4646 . . . 4 class inr
92, 8ccom 4651 . . 3 class (𝑆inr)
106, 9cun 3142 . 2 class ((𝑅inl) ∪ (𝑆inr))
113, 10wceq 1364 1 wff case(𝑅, 𝑆) = ((𝑅inl) ∪ (𝑆inr))
Colors of variables: wff set class
This definition is referenced by:  casefun  7118  casedm  7119  caserel  7120  caseinj  7122  caseinl  7124  caseinr  7125
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