Theorem nfriOLD 2189

Description: Obsolete proof of nf5ri 2065 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfriOLD.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfriOLD	⊢ (𝜑 → ∀𝑥𝜑)

Proof of Theorem nfriOLD

Step	Hyp	Ref	Expression
1		nfriOLD.1	. 2 ⊢ Ⅎ𝑥𝜑
2		nfrOLD 2188	. 2 ⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))
3	1, 2	ax-mp 5	1 ⊢ (𝜑 → ∀𝑥𝜑)

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:  alimdOLD  2191  alrimiOLD  2192  eximdOLD  2197  nexdOLD  2198  albidOLD  2199  exbidOLD  2200  19.3OLD  2202  nfim1OLD  2228  hbanOLD  2240  hb3anOLD  2241