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Theorem pssirr 3407
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 pm3.24 853 . 2  |-  -.  ( A  C_  A  /\  -.  A  C_  A )
2 dfpss3 3393 . 2  |-  ( A 
C.  A  <->  ( A  C_  A  /\  -.  A  C_  A ) )
31, 2mtbir 291 1  |-  -.  A  C.  A
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 359    C_ wss 3280    C. wpss 3281
This theorem is referenced by:  porpss  6485  ltsopr  8865
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-ne 2569  df-in 3287  df-ss 3294  df-pss 3296
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