Theorem 3anim1i

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009)

	Ref	Expression
Hypothesis	3animi.1	$$⊢\phi \to \psi$$
Assertion	3anim1i	$$⊢\left(\phi \wedge \chi \wedge \theta \right)\to \left(\psi \wedge \chi \wedge \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		3animi.1	$$⊢\phi \to \psi$$
2		id	$$⊢\chi \to \chi$$
3		id	$$⊢\theta \to \theta$$
4	1 2 3	3anim123i	$$⊢\left(\phi \wedge \chi \wedge \theta \right)\to \left(\psi \wedge \chi \wedge \theta \right)$$