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

Theorem pssne 3386
Description: Two classes in a proper subclass relationship are not equal. (Contributed by NM, 16-Feb-2015.)
Assertion
Ref Expression
pssne  |-  ( A 
C.  B  ->  A  =/=  B )

Proof of Theorem pssne
StepHypRef Expression
1 df-pss 3279 . 2  |-  ( A 
C.  B  <->  ( A  C_  B  /\  A  =/= 
B ) )
21simprbi 451 1  |-  ( A 
C.  B  ->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    =/= wne 2550    C_ wss 3263    C. wpss 3264
This theorem is referenced by:  pssned  3388  canthp1lem2  8461  mrissmrcd  13792
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361  df-pss 3279
  Copyright terms: Public domain W3C validator