Theorem mpan9

Description: Modus ponens conjoining dissimilar antecedents. (Contributed by NM, 1-Feb-2008) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Hypotheses	mpan9.1	$$⊢\phi \to \psi$$
	mpan9.2	$$⊢\chi \to \left(\psi \to \theta \right)$$
Assertion	mpan9	$$⊢\left(\phi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mpan9.1	$$⊢\phi \to \psi$$
2		mpan9.2	$$⊢\chi \to \left(\psi \to \theta \right)$$
3	1 2	syl5	$$⊢\chi \to \left(\phi \to \theta \right)$$
4	3	impcom	$$⊢\left(\phi \wedge \chi \right)\to \theta$$