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Theorem pssirr 3740
 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 pm3.24 944 . 2 ¬ (𝐴𝐴 ∧ ¬ 𝐴𝐴)
2 dfpss3 3726 . 2 (𝐴𝐴 ↔ (𝐴𝐴 ∧ ¬ 𝐴𝐴))
31, 2mtbir 312 1 ¬ 𝐴𝐴
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∧ wa 383   ⊆ wss 3607   ⊊ wpss 3608 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-ne 2824  df-in 3614  df-ss 3621  df-pss 3623 This theorem is referenced by:  porpss  6983  ltsopr  9892
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