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Theorem con1dc 746
Description: Contraposition for a decidable proposition. Based on theorem *2.15 of [WhiteheadRussell] p. 102. (Contributed by Jim Kingdon, 29-Mar-2018.)
Assertion
Ref Expression
con1dc (DECID φ → ((¬ φψ) → (¬ ψφ)))

Proof of Theorem con1dc
StepHypRef Expression
1 notnot1 547 . . 3 (ψ → ¬ ¬ ψ)
21imim2i 12 . 2 ((¬ φψ) → (¬ φ → ¬ ¬ ψ))
3 condc 740 . 2 (DECID φ → ((¬ φ → ¬ ¬ ψ) → (¬ ψφ)))
42, 3syl5 28 1 (DECID φ → ((¬ φψ) → (¬ ψφ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  DECID wdc 733
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 532  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110  df-dc 734
This theorem is referenced by:  impidc  748  simplimdc  750  con1biimdc  760  con1bdc  765  pm3.13dc  854  necon1aidc  2234  necon1bidc  2235  necon1addc  2259  necon1bddc  2260
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