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Theorem pssssd 3366
Description: Deduce subclass from proper subclass. (Contributed by NM, 29-Feb-1996.)
Hypothesis
Ref Expression
pssssd.1 (φAB)
Assertion
Ref Expression
pssssd (φA B)

Proof of Theorem pssssd
StepHypRef Expression
1 pssssd.1 . 2 (φAB)
2 pssss 3364 . 2 (ABA B)
31, 2syl 15 1 (φA B)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wss 3257  wpss 3258
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 177  df-an 360  df-pss 3261
This theorem is referenced by:  sfinltfin  4535
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