Theorem bj-stdpc5

Description: More direct proof of stdpc5 . (Contributed by BJ, 15-Sep-2018) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-stdpc5.1	⊢ Ⅎ 𝑥 𝜑
Assertion	bj-stdpc5	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-stdpc5.1	⊢ Ⅎ 𝑥 𝜑
2		stdpc5t	⊢ ( Ⅎ 𝑥 𝜑 → ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜓 ) ) )
3	1 2	ax-mp	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜓 ) )