Theorem pssssd 2706

Description: Deduce subclass from proper subclass.

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 2705	. 2 |- (A C. B -> A C_ B)
3	1, 2	syl 12	1 |- (ph -> A C_ B)

Syntax hints:   -> wi 3   C_ wss 2593   C. wpss 2594

This theorem is referenced by:  elprpq 6247  genpss 6259  ltexprlem7 6300

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242  df-pss 2607

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