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Theorem imp5g 346
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
imp5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp5g ((𝜑𝜓) → (((𝜒𝜃) ∧ 𝜏) → 𝜂))

Proof of Theorem imp5g
StepHypRef Expression
1 imp5.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21imp 119 . 2 ((𝜑𝜓) → (𝜒 → (𝜃 → (𝜏𝜂))))
32imp4c 337 1 ((𝜑𝜓) → (((𝜒𝜃) ∧ 𝜏) → 𝜂))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104
This theorem is referenced by: (None)
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