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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===
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>
