Definition df-pss 2045

Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. Other possible definitions are given by dfpss2 2123 and dfpss3 2124.

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 2038	. 2 wff A ⊂ B
4	1, 2	wss 2037	. . 3 wff A ⊆ B
5	1, 2	wne 1577	. . 3 wff A ≠ B
6	4, 5	wa 223	. 2 wff (A ⊆ B ⋀ A ≠ B)
7	3, 6	wb 146	1 wff (A ⊂ B ↔ (A ⊆ B ⋀ A ≠ B))

This definition is referenced by:  dfpss2 2123  psseq1 2125  psseq2 2126  pssss 2133  0pss 2298  pssnel 2321  ordelpss 2965  ominf 4508  inf3lem2 4586  inf3lem4 4588  infeq5 4593  ch0psst 9284

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