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Definition df-rpss 6812
Description: Define a relation which corresponds to proper subsethood df-pss 3555 on sets. This allows us to use proper subsethood with general concepts that require relations, such as strict ordering, see sorpss 6817. (Contributed by Stefan O'Rear, 2-Nov-2014.)
Assertion
Ref Expression
df-rpss [] = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-rpss
StepHypRef Expression
1 crpss 6811 . 2 class []
2 vx . . . . 5 setvar 𝑥
32cv 1473 . . . 4 class 𝑥
4 vy . . . . 5 setvar 𝑦
54cv 1473 . . . 4 class 𝑦
63, 5wpss 3540 . . 3 wff 𝑥𝑦
76, 2, 4copab 4636 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
81, 7wceq 1474 1 wff [] = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relrpss  6813  brrpssg  6814
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