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Theorem imp5q 32608
Description: A triple importation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
3imp5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp5q ((𝜑𝜓) → ((𝜒𝜃𝜏) → 𝜂))

Proof of Theorem imp5q
StepHypRef Expression
1 3imp5.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21imp 444 . 2 ((𝜑𝜓) → (𝜒 → (𝜃 → (𝜏𝜂))))
323impd 1442 1 ((𝜑𝜓) → ((𝜒𝜃𝜏) → 𝜂))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1072
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 385  df-3an 1074
This theorem is referenced by:  elicc3  32613
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