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	⊢ ( 𝜑 → 𝜓 )
	anim12i.2	⊢ ( 𝜒 → 𝜃 )
Assertion	anim12i	⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		anim12i.1	⊢ ( 𝜑 → 𝜓 )
2		anim12i.2	⊢ ( 𝜒 → 𝜃 )
3		id	⊢ ( ( 𝜓 ∧ 𝜃 ) → ( 𝜓 ∧ 𝜃 ) )
4	1 2 3	syl2an	⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) )