Theorem anim1d

Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994)

	Ref	Expression
Hypothesis	anim1d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	anim1d	$$⊢\phi \to \left(\left(\psi \wedge \theta \right)\to \left(\chi \wedge \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		anim1d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		idd	$$⊢\phi \to \left(\theta \to \theta \right)$$
3	1 2	anim12d	$$⊢\phi \to \left(\left(\psi \wedge \theta \right)\to \left(\chi \wedge \theta \right)\right)$$