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Theorem ad5ant14OLD 771
 Description: Obsolete version of ad5ant14 770 as of 14-Apr-2022. (Contributed by Alan Sare, 17-Oct-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ad5ant2.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
ad5ant14OLD (((((𝜑𝜃) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant14OLD
StepHypRef Expression
1 ad5ant2.1 . . . . . . . . 9 ((𝜑𝜓) → 𝜒)
21ex 402 . . . . . . . 8 (𝜑 → (𝜓𝜒))
322a1dd 51 . . . . . . 7 (𝜑 → (𝜓 → (𝜃 → (𝜏𝜒))))
43a1ddd 80 . . . . . 6 (𝜑 → (𝜓 → (𝜃 → (𝜂 → (𝜏𝜒)))))
54com45 97 . . . . 5 (𝜑 → (𝜓 → (𝜃 → (𝜏 → (𝜂𝜒)))))
65com23 86 . . . 4 (𝜑 → (𝜃 → (𝜓 → (𝜏 → (𝜂𝜒)))))
76com34 91 . . 3 (𝜑 → (𝜃 → (𝜏 → (𝜓 → (𝜂𝜒)))))
87imp 396 . 2 ((𝜑𝜃) → (𝜏 → (𝜓 → (𝜂𝜒))))
98imp41 417 1 (((((𝜑𝜃) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 385 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 199  df-an 386 This theorem is referenced by: (None)
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