Theorem mp2ani

Description: An inference based on modus ponens. (Contributed by NM, 12-Dec-2004)

	Ref	Expression
Hypotheses	mp2ani.1	$$⊢\psi$$
	mp2ani.2	$$⊢\chi$$
	mp2ani.3	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
Assertion	mp2ani	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mp2ani.1	$$⊢\psi$$
2		mp2ani.2	$$⊢\chi$$
3		mp2ani.3	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
4	1 3	mpani	$$⊢\phi \to \left(\chi \to \theta \right)$$
5	2 4	mpi	$$⊢\phi \to \theta$$