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Theorem nfdOLD 2181
 Description: Obsolete proof of nf5d 2104 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfdOLD.1 𝑥𝜑
nfdOLD.2 (𝜑 → (𝜓 → ∀𝑥𝜓))
Assertion
Ref Expression
nfdOLD (𝜑 → Ⅎ𝑥𝜓)

Proof of Theorem nfdOLD
StepHypRef Expression
1 nfdOLD.1 . . 3 𝑥𝜑
2 nfdOLD.2 . . 3 (𝜑 → (𝜓 → ∀𝑥𝜓))
31, 2alrimiOLD 2180 . 2 (𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓))
4 df-nfOLD 1712 . 2 (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
53, 4sylibr 223 1 (𝜑 → Ⅎ𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1473  ℲwnfOLD 1700 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nfOLD 1712 This theorem is referenced by:  nfdhOLD  2182  nfntOLD  2197
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