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Metamath Proof Explorer

Theorem pssssd

Description: Deduce subclass from proper subclass. (Contributed by NM, 29-Feb-1996)

		Ref	Expression
	Hypothesis	pssssd.1	$⊢ φ \to A \subset B$
	Assertion	pssssd	$⊢ φ \to A \subseteq B$

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