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Theorem npss 3379
Description: A class is not a proper subclass of another iff it satisfies a one-directional form of eqss 3287. (Contributed by Mario Carneiro, 15-May-2015.)
Assertion
Ref Expression
npss

Proof of Theorem npss
StepHypRef Expression
1 pm4.61 415 . . 3
2 dfpss2 3354 . . 3
31, 2bitr4i 243 . 2
43con1bii 321 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wa 358   wceq 1642   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-ne 2518  df-pss 3261
This theorem is referenced by: (None)
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