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Metamath Proof Explorer

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	$⊢ (Ⅎ x φ \land Ⅎ x ψ) \to Ⅎ x (φ \to ψ)$

Proof

Step	Hyp	Ref	Expression
1		simpl	$⊢ (Ⅎ x φ \land Ⅎ x ψ) \to Ⅎ x φ$
2		simpr	$⊢ (Ⅎ x φ \land Ⅎ x ψ) \to Ⅎ x ψ$
3	1 2	nfimd	$⊢ (Ⅎ x φ \land Ⅎ x ψ) \to Ⅎ x (φ \to ψ)$