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Theorem exbir 1322
Description: Exportation implication also converting head from biconditional to conditional. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
exbir (((φ ψ) → (χθ)) → (φ → (ψ → (θχ))))

Proof of Theorem exbir
StepHypRef Expression
1 bi2 121 . . 3 ((χθ) → (θχ))
21imim2i 12 . 2 (((φ ψ) → (χθ)) → ((φ ψ) → (θχ)))
32expd 245 1 (((φ ψ) → (χθ)) → (φ → (ψ → (θχ))))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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