Theorem anabsi5

Description: Absorption of antecedent into conjunction. (Contributed by NM, 11-Jun-1995) (Proof shortened by Wolf Lammen, 18-Nov-2013)

	Ref	Expression
Hypothesis	anabsi5.1	$$⊢\phi \to \left(\left(\phi \wedge \psi \right)\to \chi \right)$$
Assertion	anabsi5	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		anabsi5.1	$$⊢\phi \to \left(\left(\phi \wedge \psi \right)\to \chi \right)$$
2		simpl	$$⊢\left(\phi \wedge \psi \right)\to \phi$$
3	2 1	mpcom	$$⊢\left(\phi \wedge \psi \right)\to \chi$$