Definition df-rpss 7771

Description: Define a relation which corresponds to proper subsethood df-pss 4017 on sets. This allows to use proper subsethood with general concepts that require relations, such as strict ordering, see sorpss 7776. (Contributed by Stefan O'Rear, 2-Nov-2014.)

Assertion

Ref	Expression
df-rpss	⊢ [⊊] = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊊ 𝑦}

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-rpss

Step	Hyp	Ref	Expression
1		crpss 7770	. 2 class [⊊]
2		vx	. . . . 5 setvar 𝑥
3	2	cv 1569	. . . 4 class 𝑥
4		vy	. . . . 5 setvar 𝑦
5	4	cv 1569	. . . 4 class 𝑦
6	3, 5	wpss 4016	. . 3 wff 𝑥 ⊊ 𝑦
7	6, 2, 4	copab 5173	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊊ 𝑦}
8	1, 7	wceq 1570	1 wff [⊊] = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ⊊ 𝑦}

This definition is used by:  relrpss  7772  brrpssg  7773