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Theorem 3impexpbicomi 39186
Description: Inference associated with 3impexpbicom 39185. Derived automatically from 3impexpbicomiVD 39590. (Contributed by Alan Sare, 31-Dec-2011.)
Hypothesis
Ref Expression
3impexpbicomi.1 ((𝜑𝜓𝜒) → (𝜃𝜏))
Assertion
Ref Expression
3impexpbicomi (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))

Proof of Theorem 3impexpbicomi
StepHypRef Expression
1 3impexpbicomi.1 . . 3 ((𝜑𝜓𝜒) → (𝜃𝜏))
21bicomd 213 . 2 ((𝜑𝜓𝜒) → (𝜏𝜃))
323exp 1113 1 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  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:  sbcoreleleq  39245  sbcoreleleqVD  39592
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