Theorem pssssd

Description: Deduce subclass from proper subclass. (Contributed by NM, 29-Feb-1996)

	Ref	Expression
Hypothesis	pssssd.1	⊢ ( 𝜑 → 𝐴 ⊊ 𝐵 )
Assertion	pssssd	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		pssssd.1	⊢ ( 𝜑 → 𝐴 ⊊ 𝐵 )
2		pssss	⊢ ( 𝐴 ⊊ 𝐵 → 𝐴 ⊆ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )