Definition df-pss 1494

Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. Other possible definitions are given by dfpss2 1557 and dfpss3 1558.

Assertion

Ref	Expression
df-pss	⊢ (A ⊂ B ↔ (A ⊆ B ∧ A ≠ B))

Detailed syntax breakdown of Definition df-pss

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	wpss 1488	. 2 wff A ⊂ B
4	1, 2	wss 1487	. . 3 wff A ⊆ B
5	1, 2	wne 1190	. . 3 wff A ≠ B
6	4, 5	wa 196	. 2 wff (A ⊆ B ∧ A ≠ B)
7	3, 6	wb 127	1 wff (A ⊂ B ↔ (A ⊆ B ∧ A ≠ B))

This definition is referenced by:  dfpss2 1557  psseq1 1559  psseq2 1560  pssss 1567

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