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Theorem imp5a 441
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.) (Proof shortened by Wolf Lammen, 2-Aug-2022.)
Hypothesis
Ref Expression
imp5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp5a (𝜑 → (𝜓 → (𝜒 → ((𝜃𝜏) → 𝜂))))

Proof of Theorem imp5a
StepHypRef Expression
1 imp5.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21imp5d 440 . 2 (((𝜑𝜓) ∧ 𝜒) → ((𝜃𝜏) → 𝜂))
32exp31 420 1 (𝜑 → (𝜓 → (𝜒 → ((𝜃𝜏) → 𝜂))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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
This theorem is referenced by:  prtlem17  35892  tendospcanN  38039
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