Theorem pssne 3703

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

Step	Hyp	Ref	Expression
1		df-pss 3590	. 2 |- ( A C. B <-> ( A C_ B /\ A =/= B ) )
2	1	simprbi 480	1 |- ( A C. B -> A =/= B )

Syntax hints:   -> wi 4   =/= wne 2794   C_ wss 3574   C. wpss 3575

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 197  df-an 386  df-pss 3590

This theorem is referenced by:  pssned  3705  canthp1lem2  9475  mrissmrcd  16300