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Theorem exbir 39001
Description: Exportation implication also converting the consequent from a biconditional to an implication. Derived automatically from exbirVD 39402. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
exbir (((𝜑𝜓) → (𝜒𝜃)) → (𝜑 → (𝜓 → (𝜃𝜒))))

Proof of Theorem exbir
StepHypRef Expression
1 biimpr 210 . . 3 ((𝜒𝜃) → (𝜃𝜒))
21imim2i 16 . 2 (((𝜑𝜓) → (𝜒𝜃)) → ((𝜑𝜓) → (𝜃𝜒)))
32expd 451 1 (((𝜑𝜓) → (𝜒𝜃)) → (𝜑 → (𝜓 → (𝜃𝜒))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383
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
This theorem is referenced by: (None)
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