Theorem wl-lem-nexmo

Description: This theorem provides a basic working step in proving theorems about E* or E! . (Contributed by Wolf Lammen, 3-Oct-2019)

	Ref	Expression
Assertion	wl-lem-nexmo	$$⊢\neg \exists x\phi \to \forall x\left(\phi \to x=z\right)$$

Proof

Step	Hyp	Ref	Expression
1		alnex	$$⊢\forall x\neg \phi \leftrightarrow \neg \exists x\phi$$
2		pm2.21	$$⊢\neg \phi \to \left(\phi \to x=z\right)$$
3	2	alimi	$$⊢\forall x\neg \phi \to \forall x\left(\phi \to x=z\right)$$
4	1 3	sylbir	$$⊢\neg \exists x\phi \to \forall x\left(\phi \to x=z\right)$$