Theorem 19.36i

Description: Inference associated with 19.36 . See 19.36iv for a version requiring fewer axioms. (Contributed by NM, 24-Jun-1993)

	Ref	Expression
Hypotheses	19.36.1	⊢ Ⅎ 𝑥 𝜓
	19.36i.2	⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
Assertion	19.36i	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		19.36.1	⊢ Ⅎ 𝑥 𝜓
2		19.36i.2	⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
3	1	19.36	⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) ↔ ( ∀ 𝑥 𝜑 → 𝜓 ) )
4	2 3	mpbi	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )