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Theorem imp511 430
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
imp5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp511 ((𝜑 ∧ ((𝜓 ∧ (𝜒𝜃)) ∧ 𝜏)) → 𝜂)

Proof of Theorem imp511
StepHypRef Expression
1 imp5.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21imp4a 409 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → (𝜏𝜂))))
32imp44 415 1 ((𝜑 ∧ ((𝜓 ∧ (𝜒𝜃)) ∧ 𝜏)) → 𝜂)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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
This theorem is referenced by: (None)
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