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Theorem pssne 3866
Description: Two classes in a proper subclass relationship are not equal. (Contributed by NM, 16-Feb-2015.)
Assertion
Ref Expression
pssne (𝐴𝐵𝐴𝐵)

Proof of Theorem pssne
StepHypRef Expression
1 df-pss 3750 . 2 (𝐴𝐵 ↔ (𝐴𝐵𝐴𝐵))
21simprbi 490 1 (𝐴𝐵𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wne 2937  wss 3734  wpss 3735
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 198  df-an 385  df-pss 3750
This theorem is referenced by:  pssned  3868  canthp1lem2  9730  mrissmrcd  16569  xppss12  37932
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