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Theorem pssned 4111
Description: Proper subclasses are unequal. Deduction form of pssne 4109. (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 4109 . 2 (𝐴𝐵𝐴𝐵)
31, 2syl 17 1 (𝜑𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wne 2938  wpss 3964
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 207  df-an 396  df-pss 3983
This theorem is referenced by:  omsucne  7906  ackbij1lem15  10271  canthnumlem  10686  canthp1lem2  10691  mrieqv2d  17684  slwpss  19645  topdifinffinlem  37330  lsatssn0  38984  islshpcv  39035  lkrpssN  39145
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