Theorem anim12i

Description: Conjoin antecedents and consequents of two premises. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 14-Dec-2013)

	Ref	Expression
Hypotheses	anim12i.1	$$⊢\phi \to \psi$$
	anim12i.2	$$⊢\chi \to \theta$$
Assertion	anim12i	$$⊢\left(\phi \wedge \chi \right)\to \left(\psi \wedge \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		anim12i.1	$$⊢\phi \to \psi$$
2		anim12i.2	$$⊢\chi \to \theta$$
3		id	$$⊢\left(\psi \wedge \theta \right)\to \left(\psi \wedge \theta \right)$$
4	1 2 3	syl2an	$$⊢\left(\phi \wedge \chi \right)\to \left(\psi \wedge \theta \right)$$