Theorem pssss

Description: A proper subclass is a subclass. Theorem 10 of Suppes p. 23. (Contributed by NM, 7-Feb-1996)

	Ref	Expression
Assertion	pssss	⊢ ( 𝐴 ⊊ 𝐵 → 𝐴 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		df-pss	⊢ ( 𝐴 ⊊ 𝐵 ↔ ( 𝐴 ⊆ 𝐵 ∧ 𝐴 ≠ 𝐵 ) )
2	1	simplbi	⊢ ( 𝐴 ⊊ 𝐵 → 𝐴 ⊆ 𝐵 )