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Theorem hbimdOLD 2218
Description: Obsolete proof of hbimd 2111 as of 6-Oct-2021. (Contributed by NM, 14-May-1993.) (Proof shortened by Wolf Lammen, 3-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
hbimdOLD.1 (𝜑 → ∀𝑥𝜑)
hbimdOLD.2 (𝜑 → (𝜓 → ∀𝑥𝜓))
hbimdOLD.3 (𝜑 → (𝜒 → ∀𝑥𝜒))
Assertion
Ref Expression
hbimdOLD (𝜑 → ((𝜓𝜒) → ∀𝑥(𝜓𝜒)))

Proof of Theorem hbimdOLD
StepHypRef Expression
1 hbimdOLD.1 . . . 4 (𝜑 → ∀𝑥𝜑)
2 hbimdOLD.2 . . . 4 (𝜑 → (𝜓 → ∀𝑥𝜓))
31, 2nfdhOLD 2182 . . 3 (𝜑 → Ⅎ𝑥𝜓)
4 hbimdOLD.3 . . . 4 (𝜑 → (𝜒 → ∀𝑥𝜒))
51, 4nfdhOLD 2182 . . 3 (𝜑 → Ⅎ𝑥𝜒)
63, 5nfimdOLD 2214 . 2 (𝜑 → Ⅎ𝑥(𝜓𝜒))
76nfrdOLD 2178 1 (𝜑 → ((𝜓𝜒) → ∀𝑥(𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1473
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-10 2006  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701  df-nfOLD 1712
This theorem is referenced by: (None)
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