Theorem pssexg

Description: The proper subset of a set is also a set. (Contributed by Steven Nguyen, 17-Jul-2022)

	Ref	Expression
Assertion	pssexg	⊢ ( ( 𝐴 ⊊ 𝐵 ∧ 𝐵 ∈ 𝐶 ) → 𝐴 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		pssss	⊢ ( 𝐴 ⊊ 𝐵 → 𝐴 ⊆ 𝐵 )
2		ssexg	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ 𝐵 ∈ 𝐶 ) → 𝐴 ∈ V )
3	1 2	sylan	⊢ ( ( 𝐴 ⊊ 𝐵 ∧ 𝐵 ∈ 𝐶 ) → 𝐴 ∈ V )