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Theorem nfdOLD 2192
Description: Obsolete proof of nf5d 2115 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 2191 . 2 (𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓))
4 df-nfOLD 1718 . 2 (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
53, 4sylibr 224 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wnfOLD 1706
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-ex 1702  df-nfOLD 1718
This theorem is referenced by:  nfdhOLD  2193  nfntOLD  2208
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