Theorem pssssd 2144

Description: Deduce subclass from proper subclass.

Hypothesis

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

Assertion

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

Proof of Theorem pssssd

Step	Hyp	Ref	Expression
1		pssssd.1	. 2 |- (ph -> A (. B)
2		pssss 2143	. 2 |- (A (. B -> A (_ B)
3	1, 2	syl 10	1 |- (ph -> A (_ B)

Syntax hints:   -> wi 3   (_ wss 2047   (. wpss 2048

This theorem is referenced by:  elprpq 5095  genpss 5107  ltexprlem7 5148

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 147  df-an 225  df-pss 2055

Copyright terms: Public domain