Theorem emptyex

Description: On the empty domain, any existentially quantified formula is false. (Contributed by Wolf Lammen, 21-Jan-2024)

	Ref	Expression
Assertion	emptyex	$$⊢\neg \exists x\top \to \neg \exists x\phi$$

Proof

Step	Hyp	Ref	Expression
1		trud	$$⊢\phi \to \top$$
2	1	eximi	$$⊢\exists x\phi \to \exists x\top$$
3	2	con3i	$$⊢\neg \exists x\top \to \neg \exists x\phi$$