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Theorem ex3 1340
 Description: Apply ex 413 to a hypothesis with a 3-right-nested conjunction antecedent, with the antecedent of the assertion being a triple conjunction rather than a 2-right-nested conjunction. (Contributed by Alan Sare, 22-Apr-2018.)
Hypothesis
Ref Expression
ex3.1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
ex3 ((𝜑𝜓𝜒) → (𝜃𝜏))

Proof of Theorem ex3
StepHypRef Expression
1 ex3.1 . . 3 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
21ex 413 . 2 (((𝜑𝜓) ∧ 𝜒) → (𝜃𝜏))
323impa 1104 1 ((𝜑𝜓𝜒) → (𝜃𝜏))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1081 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 208  df-an 397  df-3an 1083 This theorem is referenced by:  fzrevral  12982  pthdepisspth  27430  cyc3genpm  30708  iunconnlem2  41134
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