Theorem ss2abdvOLD

Description: Obsolete version of ss2abdv as of 28-Jun-2024. (Contributed by NM, 29-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ss2abdvOLD.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	ss2abdvOLD	⊢ ( 𝜑 → { 𝑥 ∣ 𝜓 } ⊆ { 𝑥 ∣ 𝜒 } )

Proof

Step	Hyp	Ref	Expression
1		ss2abdvOLD.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	alrimiv	⊢ ( 𝜑 → ∀ 𝑥 ( 𝜓 → 𝜒 ) )
3		ss2ab	⊢ ( { 𝑥 ∣ 𝜓 } ⊆ { 𝑥 ∣ 𝜒 } ↔ ∀ 𝑥 ( 𝜓 → 𝜒 ) )
4	2 3	sylibr	⊢ ( 𝜑 → { 𝑥 ∣ 𝜓 } ⊆ { 𝑥 ∣ 𝜒 } )