12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Saturday April 12, 2025
Jump to navigationJump to search→Equational form: spacing
Line 55:
Line 55:
<center>+<p><math>((p \Rightarrow q) \Rightarrow p) \Leftrightarrow p</math></p>+</center>+<center>+<p><math>p \Rightarrow ((p \Rightarrow q) \Rightarrow p)</math></p>+</center>+
A stronger form of Peirce's law also holds, in which the final implication is observed to be reversible:
A stronger form of Peirce's law also holds, in which the final implication is observed to be reversible:
−{| align="center" cellpadding="10"
−| <math>((p \Rightarrow q) \Rightarrow p) \Leftrightarrow p</math>
−|}
===Proof 1===
===Proof 1===
Line 63:
Line 63:
Given what precedes, it remains to show that:
Given what precedes, it remains to show that:
−{| align="center" cellpadding="10"
−| <math>p \Rightarrow ((p \Rightarrow q) \Rightarrow p)</math>
−|}
But this is immediate, since <math>p \Rightarrow (r \Rightarrow p)</math> for any proposition <math>r.\!</math>
But this is immediate, since <math>p \Rightarrow (r \Rightarrow p)</math> for any proposition <math>r.\!</math>
