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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 ⊆ ( 𝐵 ∖ 𝐶 ) → 𝐴 ⊆ 𝐵 )

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝐴 ⊆ ( 𝐵 ∖ 𝐶 ) → 𝐴 ⊆ ( 𝐵 ∖ 𝐶 ) )
2		difss	⊢ ( 𝐵 ∖ 𝐶 ) ⊆ 𝐵
3	1 2	sstrdi	⊢ ( 𝐴 ⊆ ( 𝐵 ∖ 𝐶 ) → 𝐴 ⊆ 𝐵 )