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Theorem pssirr 3276
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 pm3.24 852 . 2  |-  -.  ( A  C_  A  /\  -.  A  C_  A )
2 dfpss3 3262 . 2  |-  ( A 
C.  A  <->  ( A  C_  A  /\  -.  A  C_  A ) )
31, 2mtbir 290 1  |-  -.  A  C.  A
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 358    C_ wss 3152    C. wpss 3153
This theorem is referenced by:  porpss  6281  ltsopr  8656
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-ne 2448  df-in 3159  df-ss 3166  df-pss 3168
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