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Theorem ad5ant134OLD 1466
Description: Obsolete version of ad5ant134 1465 as of 23-Jun-2022. (Contributed by Alan Sare, 17-Oct-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ad5ant.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad5ant134OLD (((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)

Proof of Theorem ad5ant134OLD
StepHypRef Expression
1 ad5ant.1 . . . . . . . . 9 ((𝜑𝜓𝜒) → 𝜃)
213exp 1111 . . . . . . . 8 (𝜑 → (𝜓 → (𝜒𝜃)))
32a1ddd 80 . . . . . . 7 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
43a1ddd 80 . . . . . 6 (𝜑 → (𝜓 → (𝜒 → (𝜂 → (𝜏𝜃)))))
54com45 97 . . . . 5 (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜂𝜃)))))
65com34 91 . . . 4 (𝜑 → (𝜓 → (𝜏 → (𝜒 → (𝜂𝜃)))))
76com23 86 . . 3 (𝜑 → (𝜏 → (𝜓 → (𝜒 → (𝜂𝜃)))))
87imp 393 . 2 ((𝜑𝜏) → (𝜓 → (𝜒 → (𝜂𝜃))))
98imp41 412 1 (((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1070
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 197  df-an 383  df-3an 1072
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator