Symbols relating to logic and proofs

The following symbols may be used anywhere in text∶
Description
Symbol
Grafstate code
AND
⋀
\^
OR
⋁
\v
NOT
¬
\!
XOR
⊕
(+)
NOR
\!v
NAND
\!^
Logical only if
⟶
->
Logical if
⟵
<-
Logical if and only if
⟷
<->
Only if
implies
⟹
=>
If
is implied by
⟸
<=
If and only if
⟺
<=>
Equivalent
≡
==
Not equivalent
≢
!==
Existential quantifier
there exists
∃
\E
There does not exist
¬∃
\!E
Uniqueness quantifier
there exists exactly one
∃!
\E!
Universal quantifier
for all
∀
\A
Not for all
¬∀
\!A
Therefore
∴
\so
Because
∵
\bc}
Entails (syntax)
\GSSYM derives ;
|-
Does not entail
\GSSYM notderives ;
!|-
End of proof

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\qed