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Theorem ex3 1255
Description: Apply ex 449 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 449 . 2 (((𝜑𝜓) ∧ 𝜒) → (𝜃𝜏))
323impa 1251 1 ((𝜑𝜓𝜒) → (𝜃𝜏))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1031
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 196  df-an 385  df-3an 1033
This theorem is referenced by:  iunconlem2  37987  pthdepissPth  40933
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