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Theorem con2d 535
Description: A contraposition deduction. (Contributed by NM, 19-Aug-1993.) (Revised by NM, 12-Feb-2013.)
Hypothesis
Ref Expression
con2d.1 (φ → (ψ → ¬ χ))
Assertion
Ref Expression
con2d (φ → (χ → ¬ ψ))

Proof of Theorem con2d
StepHypRef Expression
1 con2d.1 . . . 4 (φ → (ψ → ¬ χ))
2 ax-in2 527 . . . 4 χ → (χ → ¬ ψ))
31, 2syl6 27 . . 3 (φ → (ψ → (χ → ¬ ψ)))
43com23 70 . 2 (φ → (χ → (ψ → ¬ ψ)))
5 pm2.01 528 . 2 ((ψ → ¬ ψ) → ¬ ψ)
64, 5syl6 27 1 (φ → (χ → ¬ ψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem is referenced by:  mt2d  536  con3d  541  pm3.2im  544  con2  550  pm2.65  563  con1bidc  759  exists2  1851
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 526  ax-in2 527
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