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Theorem con1biimdc 766
Description: Contraposition. (Contributed by Jim Kingdon, 4-Apr-2018.)
Assertion
Ref Expression
con1biimdc (DECID φ → ((¬ φψ) → (¬ ψφ)))

Proof of Theorem con1biimdc
StepHypRef Expression
1 bi1 111 . . 3 ((¬ φψ) → (¬ φψ))
2 con1dc 752 . . 3 (DECID φ → ((¬ φψ) → (¬ ψφ)))
31, 2syl5 28 . 2 (DECID φ → ((¬ φψ) → (¬ ψφ)))
4 bi2 121 . . . 4 ((¬ φψ) → (ψ → ¬ φ))
54con2d 554 . . 3 ((¬ φψ) → (φ → ¬ ψ))
65a1i 9 . 2 (DECID φ → ((¬ φψ) → (φ → ¬ ψ)))
73, 6impbidd 118 1 (DECID φ → ((¬ φψ) → (¬ ψφ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98  DECID wdc 741
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by:  con1bidc  767  con1biddc  769
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