Theorem pssss 3365

Description: A proper subclass is a subclass. Theorem 10 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.)

Assertion

Ref	Expression
pssss	|- (A C. B -> A C_ B)

Proof of Theorem pssss

Step	Hyp	Ref	Expression
1		df-pss 3262	. 2 |- (A C. B <-> (A C_ B /\ A =/= B))
2	1	simplbi 446	1 |- (A C. B -> A C_ 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:  pssssd  3367  sspss  3369  pssn2lp  3371  psstr  3374