Theorem nfimdOLDOLD 1942

Description: Obsolete version of nfimd 1940 as of 6-Jul-2022. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) df-nf 1828 changed. (Revised by Wolf Lammen, 18-Sep-2021.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
nfimdOLDOLD.1	⊢ (𝜑 → Ⅎ𝑥𝜓)
nfimdOLDOLD.2	⊢ (𝜑 → Ⅎ𝑥𝜒)

Assertion

Ref	Expression
nfimdOLDOLD	⊢ (𝜑 → Ⅎ𝑥(𝜓 → 𝜒))

Proof of Theorem nfimdOLDOLD

Step	Hyp	Ref	Expression
1		nfimdOLDOLD.1	. 2 ⊢ (𝜑 → Ⅎ𝑥𝜓)
2		nfimdOLDOLD.2	. 2 ⊢ (𝜑 → Ⅎ𝑥𝜒)
3		nfimt 1941	. 2 ⊢ ((Ⅎ𝑥𝜓 ∧ Ⅎ𝑥𝜒) → Ⅎ𝑥(𝜓 → 𝜒))
4	1, 2, 3	syl2anc 579	1 ⊢ (𝜑 → Ⅎ𝑥(𝜓 → 𝜒))

Syntax hints:   → wi 4  Ⅎwnf 1827

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824  df-nf 1828

This theorem is referenced by: (None)