Theorem pssss 3039

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 2933	. 2 |- ( A C. B <-> ( A C_ B /\ A =/= B ) )
2	1	simplbi 259	1 |- ( A C. B -> A C_ 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

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

This theorem is referenced by:  pssssd  3041  sspssr  3043  pssn2lp  3045  sspsstrir  3046  psstr  3049  sspsstr  3050  psssstr  3051