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Theorem pssirr 3044
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 pm3.24 627 . 2  |-  -.  ( A  C_  A  /\  -.  A  C_  A )
2 dfpss3 3030 . 2  |-  ( A 
C.  A  <->  ( A  C_  A  /\  -.  A  C_  A ) )
31, 2mtbir 596 1  |-  -.  A  C.  A
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 97    C_ wss 2917    C. wpss 2918
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ne 2206  df-in 2924  df-ss 2931  df-pss 2933
This theorem is referenced by: (None)
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