Leibniz Logic help

  • #1
need to prove this

[tex]
\frac{\urcorner P \equiv false}{P \equiv true}
[/tex]

here is what I did
using Leibniz

[tex]
\frac{X \equiv Y}{E[z:=X] \equiv E[z:=Y]}
[/tex]

[tex]
X=\urcorner P
[/tex]

[tex]
Y=false
[/tex]

[tex]
E:\urcorner z
[/tex]

[tex]
z=z
[/tex]

[tex]
\frac{\urcorner P \equiv false}{\urcorner\urcorner P \equiv \urcorner false}
[/tex]

since [tex]\urcorner\urcorner P \equiv P[/tex]
and [tex]\urcorner false \equiv true [/tex]

[tex]
\frac{\urcorner P \equiv false}{P \equiv true}
[/tex]

is this a proof?
 

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