Theorem 19.23h

Description: Theorem 19.23 of Margaris p. 90. See 19.23 . (Contributed by NM, 24-Jan-1993) (Revised by Mario Carneiro, 24-Sep-2016) (Proof shortened by Wolf Lammen, 1-Jan-2018)

	Ref	Expression
Hypothesis	19.23h.1	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
Assertion	19.23h	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) ↔ ( ∃ 𝑥 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		19.23h.1	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
2	1	nf5i	⊢ Ⅎ 𝑥 𝜓
3	2	19.23	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) ↔ ( ∃ 𝑥 𝜑 → 𝜓 ) )