Theorem pm5.1im

Description: Two propositions are equivalent if they are both true. Closed form of 2th . Equivalent to a biimp -like version of the xor-connective. This theorem stays true, no matter how you permute its operands. This is evident from its sharper version ( ph <-> ( ps <-> ( ph <-> ps ) ) ) . (Contributed by Wolf Lammen, 12-May-2013)

	Ref	Expression
Assertion	pm5.1im	$$⊢\phi \to \left(\psi \to \left(\phi \leftrightarrow \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-1	$$⊢\psi \to \left(\phi \to \psi \right)$$
2		ax-1	$$⊢\phi \to \left(\psi \to \phi \right)$$
3	1 2	impbid21d	$$⊢\phi \to \left(\psi \to \left(\phi \leftrightarrow \psi \right)\right)$$