User:Philogo/sandbox

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Logic: ¬ ∧ ∨ ∃ ∀ ¬ ∧ ∨ ∃ ∀
&not
Failed to parse (syntax error): &not


<math>\not\equiv</math>: \not\equiv mess about
<math>A\not \models_L X</math>: A\not \models_L X
A \models_L X implies A \vdash_S X
A \models_L X
A \vdash_S X
↑ or or | or ↑


¬
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||material equivalence | rowspan=3|A ⇔ B means A is true if B is true and A is false if B is false. | rowspan=3|x + 5 = y +2  ⇔  x + 3 = y ! rowspan="3" |8660

8596 ! rowspan="3" | &hArr;
&equiv;
&harr;

! rowspan="3" |

\Leftrightarrow\Leftrightarrow
\equiv\equiv
\leftrightarrow\leftarrow

|-

  1. 1 A ⇔ B
  2. 2
  3. 3 &hArr;
    &equiv;
    &harr;
  4. 4
    \Leftrightarrow\Leftrightarrow
    \equiv\equiv
    \leftrightarrow\leftarrow
  5. 5
    \Leftrightarrow
  6. 6 \equiv
  7. 7 \Leftrightarrow
  8. 8 T \models B,
  9. 9 T \implies B
  10. 10 T \therefore B
  11. 11 T \models B,
  12. 12  \models ,
  13. 13 T  \models B
  14. 14 The inference rule called Universal Generalization is characteristic of the predicate calculus. It can be stated as
if \vdash \varphi, then \vdash \forall x \, \varphi

Which reads: if φ is a theorem, then "for every x, φ" is a theorem as well.

  1. \vdash \forall x \, \varphi
  2. \vdash \forall x \, \varphi
  3. \vdash
  4. \vdash
  5. \varphi

These cannopt be raad at work:- they look tiny & wierd

  • {{nor-}} -
  • {{nand}} -
  • {{cnv}} -

these look like boxes:-

  • {{cni}} -
  • {{nonimp}} -

try

(\equiv or \leftrightarrow) \equiv