Theorem ax5e

Description: A rephrasing of ax-5 using the existential quantifier. (Contributed by Wolf Lammen, 4-Dec-2017)

	Ref	Expression
Assertion	ax5e	⊢ ( ∃ 𝑥 𝜑 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax-5	⊢ ( ¬ 𝜑 → ∀ 𝑥 ¬ 𝜑 )
2		eximal	⊢ ( ( ∃ 𝑥 𝜑 → 𝜑 ) ↔ ( ¬ 𝜑 → ∀ 𝑥 ¬ 𝜑 ) )
3	1 2	mpbir	⊢ ( ∃ 𝑥 𝜑 → 𝜑 )