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Theorem xornan 1613
Description: XOR implies NAND. (Contributed by BJ, 19-Apr-2019.)
Assertion
Ref Expression
xornan ((𝜑𝜓) → ¬ (𝜑𝜓))

Proof of Theorem xornan
StepHypRef Expression
1 xor2 1611 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
21simprbi 483 1 ((𝜑𝜓) → ¬ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 382  wa 383  wxo 1605
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 197  df-or 384  df-an 385  df-xor 1606
This theorem is referenced by:  xornan2  1614  mptxor  1835
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