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Theorem pssirr 4065
Description: Proper subclass is irreflexive. Theorem 7 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
pssirr ¬ 𝐴𝐴

Proof of Theorem pssirr
StepHypRef Expression
1 pm3.24 404 . 2 ¬ (𝐴𝐴 ∧ ¬ 𝐴𝐴)
2 dfpss3 4051 . 2 (𝐴𝐴 ↔ (𝐴𝐴 ∧ ¬ 𝐴𝐴))
31, 2mtbir 323 1 ¬ 𝐴𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wa 397  wss 3915  wpss 3916
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-ne 2945  df-v 3450  df-in 3922  df-ss 3932  df-pss 3934
This theorem is referenced by:  porpss  7669  ltsopr  10975
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