Theorem pssned 3042

Description: Proper subclasses are unequal. Deduction form of pssne 3040. (Contributed by David Moews, 1-May-2017.)

Hypothesis

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

Assertion

Ref	Expression
pssned	|- ( ph -> A =/= B )

Proof of Theorem pssned

Step	Hyp	Ref	Expression
1		pssssd.1	. 2 |- ( ph -> A C. B )
2		pssne 3040	. 2 |- ( A C. B -> A =/= B )
3	1, 2	syl 14	1 |- ( ph -> A =/= B )

Syntax hints:   -> wi 4   =/= wne 2204   C. wpss 2918

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100

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

This theorem is referenced by: (None)