Metamath Proof Explorer

Theorem pssned

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

Ref Expression
Hypothesis pssssd.1 
|- ( ph -> A C. B )
Assertion pssned 
|- ( ph -> A =/= B )

Proof

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