Theorem pssned

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

	Ref	Expression
Hypothesis	pssssd.1	$$⊢\phi \to A\subset B$$
Assertion	pssned	$$⊢\phi \to A\ne B$$

Proof

Step	Hyp	Ref	Expression
1		pssssd.1	$$⊢\phi \to A\subset B$$
2		pssne	$$⊢A\subset B\to A\ne B$$
3	1 2	syl	$$⊢\phi \to A\ne B$$