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Theorem nic-idbl 1451
Description: Double the terms. Since doubling is the same as negation, this can be viewed as a contraposition inference. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Ref Expression
nic-idbl.1 (φ (ψ ψ))
Ref Expression
nic-idbl ((ψ ψ) ((φ φ) (φ φ)))

Proof of Theorem nic-idbl
StepHypRef Expression
1 nic-idbl.1 . . 3 (φ (ψ ψ))
21nic-imp 1440 . 2 ((ψ ψ) ((φ ψ) (φ ψ)))
31nic-imp 1440 . 2 ((φ ψ) ((φ φ) (φ φ)))
42, 3nic-ich 1450 1 ((ψ ψ) ((φ φ) (φ φ)))
Colors of variables: wff setvar class
Syntax hints:   wnan 1287
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-nan 1288
This theorem is referenced by:  nic-luk1  1456
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