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 ( 𝜑𝐴𝐵 )
Assertion pssned ( 𝜑𝐴𝐵 )

Proof

Step Hyp Ref Expression
1 pssssd.1 ( 𝜑𝐴𝐵 )
2 pssne ( 𝐴𝐵𝐴𝐵 )
3 1 2 syl ( 𝜑𝐴𝐵 )