MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pssne Structured version   Visualization version   GIF version

Theorem pssne 3665
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 3556 . 2 (𝐴𝐵 ↔ (𝐴𝐵𝐴𝐵))
21simprbi 479 1 (𝐴𝐵𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wne 2780  wss 3540  wpss 3541
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 196  df-an 385  df-pss 3556
This theorem is referenced by:  pssned  3667  canthp1lem2  9354  mrissmrcd  16123
  Copyright terms: Public domain W3C validator