Theorem pssned 3368

Description: Proper subclasses are unequal. Deduction form of pssne 3366. (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 3366	. 2 |- (A C. B -> A =/= B)
3	1, 2	syl 15	1 |- (ph -> A =/= B)

Syntax hints:   -> wi 4   =/= wne 2517   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: (None)