Theorem stdpc5t

Description: Closed form of stdpc5 . (Possible to place it before 19.21t and use it to prove 19.21t ). (Contributed by BJ, 15-Sep-2018) (Proof modification is discouraged.)

	Ref	Expression
Assertion	stdpc5t	⊢ ( Ⅎ 𝑥 𝜑 → ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		nf5r	⊢ ( Ⅎ 𝑥 𝜑 → ( 𝜑 → ∀ 𝑥 𝜑 ) )
2		alim	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → ∀ 𝑥 𝜓 ) )
3	1 2	syl9	⊢ ( Ⅎ 𝑥 𝜑 → ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜓 ) ) )