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Theorem imp55 354
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
imp5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp55 (((𝜑 ∧ (𝜓 ∧ (𝜒𝜃))) ∧ 𝜏) → 𝜂)

Proof of Theorem imp55
StepHypRef Expression
1 imp5.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21imp4a 342 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → (𝜏𝜂))))
32imp42 347 1 (((𝜑 ∧ (𝜓 ∧ (𝜒𝜃))) ∧ 𝜏) → 𝜂)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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