Theorem pssne

Description: Two classes in a proper subclass relationship are not equal. (Contributed by NM, 16-Feb-2015)

	Ref	Expression
Assertion	pssne	$$⊢A\subset B\to A\ne B$$

Proof

Step	Hyp	Ref	Expression
1		df-pss	$$⊢A\subset B\leftrightarrow \left(A\subseteq B\wedge A\ne B\right)$$
2	1	simprbi	$$⊢A\subset B\to A\ne B$$