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Theorem pssne 3272
Description: Two classes in a proper subclass relationship are not equal. (Contributed by NM, 16-Feb-2015.)
Assertion
Ref Expression
pssne  |-  ( A 
C.  B  ->  A  =/=  B )

Proof of Theorem pssne
StepHypRef Expression
1 df-pss 3168 . 2  |-  ( A 
C.  B  <->  ( A  C_  B  /\  A  =/= 
B ) )
21simprbi 450 1  |-  ( A 
C.  B  ->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    =/= wne 2446    C_ wss 3152    C. wpss 3153
This theorem is referenced by:  pssned  3274  ackbij1lem15  7860  canthnumlem  8270  canthp1lem2  8275  mrissmrcd  13542  islshpcv  29243  lkrpssN  29353
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-pss 3168
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