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Theorem xornan 1503
Description: XOR implies NAND. (Contributed by BJ, 19-Apr-2019.)
Assertion
Ref Expression
xornan ((𝜑𝜓) → ¬ (𝜑𝜓))

Proof of Theorem xornan
StepHypRef Expression
1 xor2 1501 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
21simprbi 497 1 ((𝜑𝜓) → ¬ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 396  wo 841  wxo 1495
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 208  df-an 397  df-or 842  df-xor 1496
This theorem is referenced by:  xornan2  1504  mptxor  1761
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