Theorem ibib

Implication in terms of implication and biconditional. (Contributed by NM, 31-Mar-1994.) (Proof shortened by Wolf Lammen, 24-Jan-2013.)

Conclusion

\( \vdash \varphi \rightarrow \psi \leftrightarrow \varphi \rightarrow (\varphi \leftrightarrow \psi) \)

Proof

pm5.501

pm5.74i _