Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  pssirr Structured version   GIF version

Theorem pssirr 3021
 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 pm3.24 614 . 2 ¬ (AA ¬ AA)
2 dfpss3 3007 . 2 (AA ↔ (AA ¬ AA))
31, 2mtbir 583 1 ¬ AA
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∧ wa 97   ⊆ wss 2894   ⊊ wpss 2895 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-ne 2188  df-in 2901  df-ss 2908  df-pss 2910 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator