Theorem mp3an3

Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994)

	Ref	Expression
Hypotheses	mp3an3.1	$$⊢\chi$$
	mp3an3.2	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	mp3an3	$$⊢\left(\phi \wedge \psi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mp3an3.1	$$⊢\chi$$
2		mp3an3.2	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
3	2	3expia	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \theta \right)$$
4	1 3	mpi	$$⊢\left(\phi \wedge \psi \right)\to \theta$$