Theorem mpand

Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004) (Proof shortened by Wolf Lammen, 7-Apr-2013)

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

Proof

Step	Hyp	Ref	Expression
1		mpand.1	$$⊢\phi \to \psi$$
2		mpand.2	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
3	2	ancomsd	$$⊢\phi \to \left(\left(\chi \wedge \psi \right)\to \theta \right)$$
4	1 3	mpan2d	$$⊢\phi \to \left(\chi \to \theta \right)$$