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Theorem xornan2 1643
Description: XOR implies NAND (written with the connector). (Contributed by BJ, 19-Apr-2019.)
Assertion
Ref Expression
xornan2 ((𝜑𝜓) → (𝜑𝜓))

Proof of Theorem xornan2
StepHypRef Expression
1 xornan 1642 . 2 ((𝜑𝜓) → ¬ (𝜑𝜓))
2 df-nan 1610 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
31, 2sylibr 226 1 ((𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 385  wnan 1609  wxo 1634
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 199  df-an 386  df-or 875  df-nan 1610  df-xor 1635
This theorem is referenced by: (None)
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