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Theorem exbir 1341
Description: Exportation implication also converting head from biconditional to conditional. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
exbir (((𝜑𝜓) → (𝜒𝜃)) → (𝜑 → (𝜓 → (𝜃𝜒))))

Proof of Theorem exbir
StepHypRef Expression
1 bi2 125 . . 3 ((𝜒𝜃) → (𝜃𝜒))
21imim2i 12 . 2 (((𝜑𝜓) → (𝜒𝜃)) → ((𝜑𝜓) → (𝜃𝜒)))
32expd 249 1 (((𝜑𝜓) → (𝜒𝜃)) → (𝜑 → (𝜓 → (𝜃𝜒))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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