Theorem nfim1OLD 2228

Description: Obsolete proof of nfim1 2067 as of 6-Oct-2021. (Contributed by NM, 2-Jun-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 2-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
nfim1OLD.1	⊢ Ⅎ𝑥𝜑
nfim1OLD.2	⊢ (𝜑 → Ⅎ𝑥𝜓)

Assertion

Ref	Expression
nfim1OLD	⊢ Ⅎ𝑥(𝜑 → 𝜓)

Proof of Theorem nfim1OLD

Step	Hyp	Ref	Expression
1		nfim1OLD.1	. . . 4 ⊢ Ⅎ𝑥𝜑
2	1	nfriOLD 2189	. . 3 ⊢ (𝜑 → ∀𝑥𝜑)
3		nfim1OLD.2	. . . 4 ⊢ (𝜑 → Ⅎ𝑥𝜓)
4	3	nfrdOLD 2190	. . 3 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))
5	2, 4	hbim1OLD 2227	. 2 ⊢ ((𝜑 → 𝜓) → ∀𝑥(𝜑 → 𝜓))
6	5	nfiOLD 1734	1 ⊢ Ⅎ𝑥(𝜑 → 𝜓)

Syntax hints:   → wi 4  ℲwnfOLD 1709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nfOLD 1721

This theorem is referenced by:  nfimOLD  2229