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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 ∧ Ⅎ 𝑥 𝜓 ) → Ⅎ 𝑥 ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( Ⅎ 𝑥 𝜑 ∧ Ⅎ 𝑥 𝜓 ) → Ⅎ 𝑥 𝜑 )
2		simpr	⊢ ( ( Ⅎ 𝑥 𝜑 ∧ Ⅎ 𝑥 𝜓 ) → Ⅎ 𝑥 𝜓 )
3	1 2	nfimd	⊢ ( ( Ⅎ 𝑥 𝜑 ∧ Ⅎ 𝑥 𝜓 ) → Ⅎ 𝑥 ( 𝜑 → 𝜓 ) )