Theorem pssssd 3367

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 3365	. 2 |- (A C. B -> A C_ B)
3	1, 2	syl 15	1 |- (ph -> A C_ B)

Syntax hints:   -> wi 4   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:  sfinltfin  4536