Theorem eldifn

Description: Implication of membership in a class difference. (Contributed by NM, 3-May-1994)

	Ref	Expression
Assertion	eldifn	⊢ ( 𝐴 ∈ ( 𝐵 ∖ 𝐶 ) → ¬ 𝐴 ∈ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		eldif	⊢ ( 𝐴 ∈ ( 𝐵 ∖ 𝐶 ) ↔ ( 𝐴 ∈ 𝐵 ∧ ¬ 𝐴 ∈ 𝐶 ) )
2	1	simprbi	⊢ ( 𝐴 ∈ ( 𝐵 ∖ 𝐶 ) → ¬ 𝐴 ∈ 𝐶 )