Theorem pssne 3040

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 2933	. 2 |- ( A C. B <-> ( A C_ B /\ A =/= B ) )
2	1	simprbi 260	1 |- ( A C. B -> A =/= B )

Syntax hints:   -> wi 4   =/= wne 2204   C_ wss 2917   C. wpss 2918

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100

This theorem depends on definitions:  df-bi 110  df-pss 2933

This theorem is referenced by:  pssned  3042