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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	$⊢ φ \to A \subset B$
	Assertion	pssned	$⊢ φ \to A \neq B$

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