Theorem anim2d

Description: Add a conjunct to left of antecedent and consequent in a deduction. (Contributed by NM, 14-May-1993)

	Ref	Expression
Hypothesis	anim1d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	anim2d	$$⊢\phi \to \left(\left(\theta \wedge \psi \right)\to \left(\theta \wedge \chi \right)\right)$$

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	2 1	anim12d	$$⊢\phi \to \left(\left(\theta \wedge \psi \right)\to \left(\theta \wedge \chi \right)\right)$$