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Theorem pssirr 3196
Description: Proper subclass is irreflexive. Theorem 7 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
pssirr  |-  -.  A  C.  A

Proof of Theorem pssirr
StepHypRef Expression
1 pm3.24 857 . 2  |-  -.  ( A  C_  A  /\  -.  A  C_  A )
2 dfpss3 3183 . 2  |-  ( A 
C.  A  <->  ( A  C_  A  /\  -.  A  C_  A ) )
31, 2mtbir 292 1  |-  -.  A  C.  A
Colors of variables: wff set class
Syntax hints:   -. wn 5    /\ wa 360    C_ wss 3078    C. wpss 3079
This theorem is referenced by:  porpss  6133  ltsopr  8536
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-ne 2414  df-in 3085  df-ss 3089  df-pss 3091
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