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Metamath Proof Explorer

Theorem difss2d

Description: If a class is contained in a difference, it is contained in the minuend. Deduction form of difss2 . (Contributed by David Moews, 1-May-2017)

		Ref	Expression
	Hypothesis	difss2d.1	⊢ ( 𝜑 → 𝐴 ⊆ ( 𝐵 ∖ 𝐶 ) )
	Assertion	difss2d	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		difss2d.1	⊢ ( 𝜑 → 𝐴 ⊆ ( 𝐵 ∖ 𝐶 ) )
2		difss2	⊢ ( 𝐴 ⊆ ( 𝐵 ∖ 𝐶 ) → 𝐴 ⊆ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )