Definition df-pss 2026

Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. Other possible definitions are given by dfpss2 2104 and dfpss3 2105.

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 2019	. 2 wff A (. B
4	1, 2	wss 2018	. . 3 wff A (_ B
5	1, 2	wne 1561	. . 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 2104  psseq1 2106  psseq2 2107  pssss 2114  0pss 2279  pssnel 2302  ordelpss 2938  ominf 4460  inf3lem2 4538  inf3lem4 4540  infeq5 4545  ch0psst 9498

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