Theorem mpd3an3

Description: An inference based on modus ponens. (Contributed by NM, 8-Nov-2007)

	Ref	Expression
Hypotheses	mpd3an3.2	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
	mpd3an3.3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	mpd3an3	$$⊢\left(\phi \wedge \psi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mpd3an3.2	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2		mpd3an3.3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
3	2	3expa	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
4	1 3	mpdan	$$⊢\left(\phi \wedge \psi \right)\to \theta$$