Theorem nfrdOLD 2190

Description: Obsolete proof of nf5rd 2066 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
nfrdOLD.1	⊢ (𝜑 → Ⅎ𝑥𝜓)

Assertion

Ref	Expression
nfrdOLD	⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))

Proof of Theorem nfrdOLD

Step	Hyp	Ref	Expression
1		nfrdOLD.1	. 2 ⊢ (𝜑 → Ⅎ𝑥𝜓)
2		nfrOLD 2188	. 2 ⊢ (Ⅎ𝑥𝜓 → (𝜓 → ∀𝑥𝜓))
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1481  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-12 2047

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

This theorem is referenced by:  alrimddOLD  2195  nfdiOLD  2225  nfim1OLD  2228  hbimdOLD  2230  nfan1OLD  2236