Theorem pm5.15

Description: Theorem *5.15 of WhiteheadRussell p. 124. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 15-Oct-2013)

	Ref	Expression
Assertion	pm5.15	$$⊢\left(\left(\phi \leftrightarrow \psi \right)\vee \left(\phi \leftrightarrow \neg \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		xor3	$$⊢\neg \left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\phi \leftrightarrow \neg \psi \right)$$
2	1	biimpi	$$⊢\neg \left(\phi \leftrightarrow \psi \right)\to \left(\phi \leftrightarrow \neg \psi \right)$$
3	2	orri	$$⊢\left(\left(\phi \leftrightarrow \psi \right)\vee \left(\phi \leftrightarrow \neg \psi \right)\right)$$