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Theorem nfaldOLD 2311
 Description: Obsolete proof of nfald 2310 as of 16-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 6-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfald.1 𝑦𝜑
nfald.2 (𝜑 → Ⅎ𝑥𝜓)
Assertion
Ref Expression
nfaldOLD (𝜑 → Ⅎ𝑥𝑦𝜓)

Proof of Theorem nfaldOLD
StepHypRef Expression
1 nfald.1 . . 3 𝑦𝜑
2 nfald.2 . . 3 (𝜑 → Ⅎ𝑥𝜓)
31, 2alrimi 2229 . 2 (𝜑 → ∀𝑦𝑥𝜓)
4 nfnf1 2180 . . . 4 𝑥𝑥𝜓
54nfal 2300 . . 3 𝑥𝑦𝑥𝜓
6 hba1 2298 . . . 4 (∀𝑦𝑥𝜓 → ∀𝑦𝑦𝑥𝜓)
7 sp 2200 . . . . 5 (∀𝑦𝑥𝜓 → Ⅎ𝑥𝜓)
87nf5rd 2213 . . . 4 (∀𝑦𝑥𝜓 → (𝜓 → ∀𝑥𝜓))
96, 8hbald 2190 . . 3 (∀𝑦𝑥𝜓 → (∀𝑦𝜓 → ∀𝑥𝑦𝜓))
105, 9nf5d 2265 . 2 (∀𝑦𝑥𝜓 → Ⅎ𝑥𝑦𝜓)
113, 10syl 17 1 (𝜑 → Ⅎ𝑥𝑦𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1630  Ⅎwnf 1857 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-11 2183  ax-12 2196 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859 This theorem is referenced by: (None)
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