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Theorem pssirr 3870
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 pm3.24 391 . 2 ¬ (𝐴𝐴 ∧ ¬ 𝐴𝐴)
2 dfpss3 3856 . 2 (𝐴𝐴 ↔ (𝐴𝐴 ∧ ¬ 𝐴𝐴))
31, 2mtbir 314 1 ¬ 𝐴𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wa 384  wss 3734  wpss 3735
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-ne 2938  df-in 3741  df-ss 3748  df-pss 3750
This theorem is referenced by:  porpss  7143  ltsopr  10111
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