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Metamath Proof Explorer

Theorem difss2

Description: If a class is contained in a difference, it is contained in the minuend. (Contributed by David Moews, 1-May-2017)

		Ref	Expression
	Assertion	difss2	$⊢ A \subseteq B ∖ C \to A \subseteq B$

Step	Hyp	Ref	Expression
1		id	$⊢ A \subseteq B ∖ C \to A \subseteq B ∖ C$
2		difss	$⊢ B ∖ C \subseteq B$
3	1 2	sstrdi	$⊢ A \subseteq B ∖ C \to A \subseteq B$