Theorem mpdan

Description: An inference based on modus ponens. (Contributed by NM, 23-May-1999) (Proof shortened by Wolf Lammen, 22-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		mpdan.1	$$⊢\phi \to \psi$$
2		mpdan.2	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
3		id	$$⊢\phi \to \phi$$
4	3 1 2	syl2anc	$$⊢\phi \to \chi$$