Theorem pm4.15

Description: Theorem *4.15 of WhiteheadRussell p. 117. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 18-Nov-2012)

	Ref	Expression
Assertion	pm4.15	$$⊢\left(\left(\phi \wedge \psi \right)\to \neg \chi \right)\leftrightarrow \left(\left(\psi \wedge \chi \right)\to \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		con2b	$$⊢\left(\left(\psi \wedge \chi \right)\to \neg \phi \right)\leftrightarrow \left(\phi \to \neg \left(\psi \wedge \chi \right)\right)$$
2		nan	$$⊢\left(\phi \to \neg \left(\psi \wedge \chi \right)\right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\to \neg \chi \right)$$
3	1 2	bitr2i	$$⊢\left(\left(\phi \wedge \psi \right)\to \neg \chi \right)\leftrightarrow \left(\left(\psi \wedge \chi \right)\to \neg \phi \right)$$