Theorem pm5.1

Description: Two propositions are equivalent if they are both true. Theorem *5.1 of WhiteheadRussell p. 123. (Contributed by NM, 21-May-1994)

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

Proof

Step	Hyp	Ref	Expression
1		pm5.501	$$⊢\phi \to \left(\psi \leftrightarrow \left(\phi \leftrightarrow \psi \right)\right)$$
2	1	biimpa	$$⊢\left(\phi \wedge \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$