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Theorem pssirr 3071
 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 pm3.24 637 . 2 ¬ (𝐴𝐴 ∧ ¬ 𝐴𝐴)
2 dfpss3 3057 . 2 (𝐴𝐴 ↔ (𝐴𝐴 ∧ ¬ 𝐴𝐴))
31, 2mtbir 606 1 ¬ 𝐴𝐴
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∧ wa 101   ⊆ wss 2944   ⊊ wpss 2945 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-ne 2221  df-in 2951  df-ss 2958  df-pss 2960 This theorem is referenced by: (None)
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