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Theorem pssssd 4076
 Description: Deduce subclass from proper subclass. (Contributed by NM, 29-Feb-1996.)
Hypothesis
Ref Expression
pssssd.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
pssssd (𝜑𝐴𝐵)

Proof of Theorem pssssd
StepHypRef Expression
1 pssssd.1 . 2 (𝜑𝐴𝐵)
2 pssss 4074 . 2 (𝐴𝐵𝐴𝐵)
31, 2syl 17 1 (𝜑𝐴𝐵)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊆ wss 3938   ⊊ wpss 3939 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 209  df-an 399  df-pss 3956 This theorem is referenced by:  fin23lem36  9772  fin23lem39  9774  canthnumlem  10072  canthp1lem2  10077  elprnq  10415  npomex  10420  prlem934  10457  ltexprlem7  10466  wuncn  10594  mrieqv2d  16912  slwpss  18739  pgpfac1lem5  19203  lbspss  19856  lsppratlem1  19921  lsppratlem3  19923  lsppratlem4  19924  lrelat  36152  lsatcvatlem  36187
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