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Theorem pssned 3856
Description: Proper subclasses are unequal. Deduction form of pssne 3854. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
pssssd.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
pssned (𝜑𝐴𝐵)

Proof of Theorem pssned
StepHypRef Expression
1 pssssd.1 . 2 (𝜑𝐴𝐵)
2 pssne 3854 . 2 (𝐴𝐵𝐴𝐵)
31, 2syl 17 1 (𝜑𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wne 2943  wpss 3725
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 197  df-an 383  df-pss 3740
This theorem is referenced by:  ackbij1lem15  9259  canthnumlem  9673  canthp1lem2  9678  mrieqv2d  16508  slwpss  18235  topdifinffinlem  33533  lsatssn0  34812  islshpcv  34863  lkrpssN  34973
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