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Theorem pssss 3067
Description: A proper subclass is a subclass. Theorem 10 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
pssss (𝐴𝐵𝐴𝐵)

Proof of Theorem pssss
StepHypRef Expression
1 df-pss 2961 . 2 (𝐴𝐵 ↔ (𝐴𝐵𝐴𝐵))
21simplbi 263 1 (𝐴𝐵𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wne 2220  wss 2945  wpss 2946
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103
This theorem depends on definitions:  df-bi 114  df-pss 2961
This theorem is referenced by:  pssssd  3069  sspssr  3071  pssn2lp  3073  sspsstrir  3074  psstr  3077  sspsstr  3078  psssstr  3079
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