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Theorem pssned 3447
Description: Proper subclasses are unequal. Deduction form of pssne 3445. (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 3445 . 2  |-  ( A 
C.  B  ->  A  =/=  B )
31, 2syl 16 1  |-  ( ph  ->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    =/= wne 2601    C. wpss 3323
This theorem is referenced by:  ackbij1lem15  8119  canthnumlem  8528  canthp1lem2  8533  mrieqv2d  13869  slwpss  15251  lsatssn0  29874  islshpcv  29925  lkrpssN  30035
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-an 362  df-pss 3338
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