AxmPropNegElim (1.09, Axiom): A09

AxmPropNegElim (1.09) — A09

Classical propositional calculus axiom schemas (A01–A13) and Modus Ponens.

Num Entity Database Record (Vertical Field Table)

Title	A09 `#AxmPropNegElim` `#label-a09`
Classification	Axiom
Formula	0((¬⟦𝛂⟧)→(⟦𝛂⟧→⊥)) 0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/neg-conn.html}{\neg} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\alpha}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/impl-conn.html}{\rightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\alpha}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/impl-conn.html}{\rightarrow} \href{../symbols/bot-const.html}{\bot} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST	`PA9_prf`
Scheme of Types	0`((¬⟦[𝛂@Fm.Expression]⟧)→(⟦[𝛂@Fm.Expression]⟧→⊥))`
Judgements	1[(𝛂 :Fm )] 1\(\href{../symbols/image-op.html}{[} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/formula-metavariables.html}{\boldsymbol{\alpha}} \href{../symbols/typing-colon.html}{:} \href{../symbols/fm-sort.html}{\mathsf{Fm}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/image-op.html}{]} \)
Kernel Note	Negation Elimination (Contradiction to Bottom): (¬⟦𝛂⟧) → (⟦𝛂⟧ → ⊥).
Verification	Postulated (Kernel Axiom) · Standalone Entry (`AxmPropNegElim`) → · (1.09) · `#AxmPropNegElim`