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Theorem pssirr 3277
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 3263 . 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 3153    C. wpss 3154
This theorem is referenced by:  porpss  6242  ltsopr  8651
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549  ax-17 1608  ax-9 1641  ax-8 1648  ax-6 1707  ax-7 1712  ax-11 1719  ax-12 1869  ax-ext 2265
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1534  df-nf 1537  df-sb 1636  df-clab 2271  df-cleq 2277  df-clel 2280  df-ne 2449  df-in 3160  df-ss 3167  df-pss 3169
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