Theorem pm2.61dan

Description: Elimination of an antecedent. (Contributed by NM, 1-Jan-2005)

	Ref	Expression
Hypotheses	pm2.61dan.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
	pm2.61dan.2	$$⊢\left(\phi \wedge \neg \psi \right)\to \chi$$
Assertion	pm2.61dan	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.61dan.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2		pm2.61dan.2	$$⊢\left(\phi \wedge \neg \psi \right)\to \chi$$
3	1	ex	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	2	ex	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
5	3 4	pm2.61d	$$⊢\phi \to \chi$$