Theorem nfimt

Description: Closed form of nfim and nfimd . (Contributed by BJ, 20-Oct-2021) Eliminate curried form, former name nfimt2. (Revised by Wolf Lammen, 6-Jul-2022)

	Ref	Expression
Assertion	nfimt	$$⊢\left(Ⅎx\phi \wedge Ⅎx\psi \right)\to Ⅎx\left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		simpl	$$⊢\left(Ⅎx\phi \wedge Ⅎx\psi \right)\to Ⅎx\phi$$
2		simpr	$$⊢\left(Ⅎx\phi \wedge Ⅎx\psi \right)\to Ⅎx\psi$$
3	1 2	nfimd	$$⊢\left(Ⅎx\phi \wedge Ⅎx\psi \right)\to Ⅎx\left(\phi \to \psi \right)$$