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Theorem con2biddc 773
Description: A contraposition deduction. (Contributed by Jim Kingdon, 11-Apr-2018.)
Hypothesis
Ref Expression
con2biddc.1 (φ → (DECID χ → (ψ ↔ ¬ χ)))
Assertion
Ref Expression
con2biddc (φ → (DECID χ → (χ ↔ ¬ ψ)))

Proof of Theorem con2biddc
StepHypRef Expression
1 con2biddc.1 . . . 4 (φ → (DECID χ → (ψ ↔ ¬ χ)))
2 bicom 128 . . . 4 ((ψ ↔ ¬ χ) ↔ (¬ χψ))
31, 2syl6ib 150 . . 3 (φ → (DECID χ → (¬ χψ)))
43con1biddc 769 . 2 (φ → (DECID χ → (¬ ψχ)))
5 bicom 128 . 2 ((¬ ψχ) ↔ (χ ↔ ¬ ψ))
64, 5syl6ib 150 1 (φ → (DECID χ → (χ ↔ ¬ ψ)))
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:  anordc  862  xor3dc  1275
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