Theorem ssnel

Description: If not element of a set, then not element of a subset. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Assertion	ssnel	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ ¬ 𝐶 ∈ 𝐵 ) → ¬ 𝐶 ∈ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ssel2	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ 𝐶 ∈ 𝐴 ) → 𝐶 ∈ 𝐵 )
2	1	stoic1a	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ ¬ 𝐶 ∈ 𝐵 ) → ¬ 𝐶 ∈ 𝐴 )