Theorem pssssd 3041

Description: Deduce subclass from proper subclass. (Contributed by NM, 29-Feb-1996.)

Hypothesis

Ref	Expression
pssssd.1	|- ( ph -> A C. B )

Assertion

Ref	Expression
pssssd	|- ( ph -> A C_ B )

Proof of Theorem pssssd

Step	Hyp	Ref	Expression
1		pssssd.1	. 2 |- ( ph -> A C. B )
2		pssss 3039	. 2 |- ( A C. B -> A C_ B )
3	1, 2	syl 14	1 |- ( ph -> A C_ B )

Syntax hints:   -> wi 4   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: (None)