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Theorem 4animp1 38185
Description: A single hypothesis unification deduction with an assertion which is an implication with a 4-right-nested conjunction antecedent. (Contributed by Alan Sare, 30-May-2018.)
Hypothesis
Ref Expression
4animp1.1 ((𝜑𝜓𝜒) → (𝜏𝜃))
Assertion
Ref Expression
4animp1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem 4animp1
StepHypRef Expression
1 simpr 477 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜃)
2 4animp1.1 . . 3 ((𝜑𝜓𝜒) → (𝜏𝜃))
32ad4ant123 1291 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → (𝜏𝜃))
41, 3mpbird 247 1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 384  w3a 1036
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 386  df-3an 1038
This theorem is referenced by:  sineq0ALT  38656
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