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Theorem nfaldOLD 2163
Description: Obsolete proof of nfald 2162 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 2080 . 2 (𝜑 → ∀𝑦𝑥𝜓)
4 nfnf1 2028 . . . 4 𝑥𝑥𝜓
54nfal 2150 . . 3 𝑥𝑦𝑥𝜓
6 hba1 2148 . . . 4 (∀𝑦𝑥𝜓 → ∀𝑦𝑦𝑥𝜓)
7 sp 2051 . . . . 5 (∀𝑦𝑥𝜓 → Ⅎ𝑥𝜓)
87nf5rd 2064 . . . 4 (∀𝑦𝑥𝜓 → (𝜓 → ∀𝑥𝜓))
96, 8hbald 2038 . . 3 (∀𝑦𝑥𝜓 → (∀𝑦𝜓 → ∀𝑥𝑦𝜓))
105, 9nf5d 2115 . 2 (∀𝑦𝑥𝜓 → Ⅎ𝑥𝑦𝜓)
113, 10syl 17 1 (𝜑 → Ⅎ𝑥𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wnf 1705
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-10 2016  ax-11 2031  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707
This theorem is referenced by: (None)
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