Theorem pssne 3366

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 3262	. 2 |- (A C. B <-> (A C_ B /\ A =/= B))
2	1	simprbi 450	1 |- (A C. B -> A =/= B)

Syntax hints:   -> wi 4   =/= wne 2517   C_ wss 3258   C. wpss 3259

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 177  df-an 360  df-pss 3262

This theorem is referenced by:  pssned  3368