Theorem mpani

Description: An inference based on modus ponens. (Contributed by NM, 10-Apr-1994) (Proof shortened by Wolf Lammen, 19-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		mpani.1	$$⊢\psi$$
2		mpani.2	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
3	1	a1i	$$⊢\phi \to \psi$$
4	3 2	mpand	$$⊢\phi \to \left(\chi \to \theta \right)$$