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Theorem pssned 3274
Description: Proper subclasses are unequal. Deduction form of pssne 3272. (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 3272 . 2  |-  ( A 
C.  B  ->  A  =/=  B )
31, 2syl 15 1  |-  ( ph  ->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    =/= wne 2446    C. wpss 3153
This theorem is referenced by:  mrieqv2d  13541
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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