AxmPropConjLeft (1.03, Axiom): A03

AxmPropConjLeft (1.03) — A03

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

Num Entity Database Record (Vertical Field Table)

Title	A03 `#AxmPropConjLeft` `#label-a03`
Classification	Axiom
Formula	0((⟦𝛂⟧∧⟦𝛃⟧)→⟦𝛂⟧) 0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\alpha}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/and-conn.html}{\land} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\beta}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/impl-conn.html}{\rightarrow} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\alpha}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST	`PA3_prf`
Scheme of Types	0`((⟦[𝛂@Fm.Expression]⟧∧⟦[𝛃@Fm.Expression]⟧)→⟦[𝛂@Fm.Expression]⟧)`
Judgements	1[(𝛂 :Fm ), (𝛃 :Fm )] 1\(\href{../symbols/image-op.html}{[} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/formula-metavariables.html}{\boldsymbol{\alpha}} \href{../symbols/typing-colon.html}{:} \href{../symbols/fm-sort.html}{\mathsf{Fm}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/comma-delim.html}{,} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/formula-metavariables.html}{\boldsymbol{\beta}} \href{../symbols/typing-colon.html}{:} \href{../symbols/fm-sort.html}{\mathsf{Fm}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/image-op.html}{]} \)
Verification	Postulated (Kernel Axiom) · Standalone Entry (`AxmPropConjLeft`) → · (1.03) · `#AxmPropConjLeft`