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Theorem nannan 1291
Description: Lemma for handling nested 'nand's. (Contributed by Jeff Hoffman, 19-Nov-2007.)
Assertion
Ref Expression
nannan ((φ (χ ψ)) ↔ (φ → (χ ψ)))

Proof of Theorem nannan
StepHypRef Expression
1 df-nan 1288 . . 3 ((φ (χ ψ)) ↔ ¬ (φ (χ ψ)))
2 df-nan 1288 . . . 4 ((χ ψ) ↔ ¬ (χ ψ))
32anbi2i 675 . . 3 ((φ (χ ψ)) ↔ (φ ¬ (χ ψ)))
41, 3xchbinx 301 . 2 ((φ (χ ψ)) ↔ ¬ (φ ¬ (χ ψ)))
5 iman 413 . 2 ((φ → (χ ψ)) ↔ ¬ (φ ¬ (χ ψ)))
64, 5bitr4i 243 1 ((φ (χ ψ)) ↔ (φ → (χ ψ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   wa 358   wnan 1287
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-nan 1288
This theorem is referenced by:  nanim  1292  nic-mp  1436  nic-ax  1438
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