AxmPropConjIntro (1.05, Axiom): A05

AxmPropConjIntro (1.05) — A05

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

Num Entity Database Record (Vertical Field Table)

Title	A05 `#AxmPropConjIntro` `#label-a05`
Classification	Axiom
Formula	0(⟦𝛂⟧→(⟦𝛃⟧→(⟦𝛂⟧∧⟦𝛃⟧))) 0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\alpha}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/impl-conn.html}{\rightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\beta}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/impl-conn.html}{\rightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\alpha}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/and-conn.html}{\land} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\beta}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST	`PA5_prf`
Scheme of Types	0`(⟦[𝛂@Fm.Expression]⟧→(⟦[𝛃@Fm.Expression]⟧→(⟦[𝛂@Fm.Expression]⟧∧⟦[𝛃@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 (`AxmPropConjIntro`) → · (1.05) · `#AxmPropConjIntro`