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Theorem pssned 3413
Description: Proper subclasses are unequal. Deduction form of pssne 3411. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
pssssd.1  |-  ( ph  ->  A  C.  B )
Assertion
Ref Expression
pssned  |-  ( ph  ->  A  =/=  B )

Proof of Theorem pssned
StepHypRef Expression
1 pssssd.1 . 2  |-  ( ph  ->  A  C.  B )
2 pssne 3411 . 2  |-  ( A 
C.  B  ->  A  =/=  B )
31, 2syl 16 1  |-  ( ph  ->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    =/= wne 2575    C. wpss 3289
This theorem is referenced by:  ackbij1lem15  8078  canthnumlem  8487  canthp1lem2  8492  mrieqv2d  13827  slwpss  15209  lsatssn0  29497  islshpcv  29548  lkrpssN  29658
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 178  df-an 361  df-pss 3304
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