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Theorem pssirr 3352
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 3338 . 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 3228    C. wpss 3229
This theorem is referenced by:  porpss  6368  ltsopr  8746
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-ne 2523  df-in 3235  df-ss 3242  df-pss 3244
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