Theorem anim12d

Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 3-Apr-1994) (Proof shortened by Wolf Lammen, 18-Dec-2013)

	Ref	Expression
Hypotheses	anim12d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	anim12d.2	$$⊢\phi \to \left(\theta \to \tau \right)$$
Assertion	anim12d	$$⊢\phi \to \left(\left(\psi \wedge \theta \right)\to \left(\chi \wedge \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		anim12d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		anim12d.2	$$⊢\phi \to \left(\theta \to \tau \right)$$
3		idd	$$⊢\phi \to \left(\left(\chi \wedge \tau \right)\to \left(\chi \wedge \tau \right)\right)$$
4	1 2 3	syl2and	$$⊢\phi \to \left(\left(\psi \wedge \theta \right)\to \left(\chi \wedge \tau \right)\right)$$