Theorem mpd3an23

Description: An inference based on modus ponens. (Contributed by NM, 4-Dec-2006)

	Ref	Expression
Hypotheses	mpd3an23.1	$$⊢\phi \to \psi$$
	mpd3an23.2	$$⊢\phi \to \chi$$
	mpd3an23.3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	mpd3an23	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mpd3an23.1	$$⊢\phi \to \psi$$
2		mpd3an23.2	$$⊢\phi \to \chi$$
3		mpd3an23.3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
4		id	$$⊢\phi \to \phi$$
5	4 1 2 3	syl3anc	$$⊢\phi \to \theta$$