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	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	anim12d.2	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
Assertion	anim12d	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜃 ) → ( 𝜒 ∧ 𝜏 ) ) )

Proof

Step	Hyp	Ref	Expression
1		anim12d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		anim12d.2	⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
3		idd	⊢ ( 𝜑 → ( ( 𝜒 ∧ 𝜏 ) → ( 𝜒 ∧ 𝜏 ) ) )
4	1 2 3	syl2and	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜃 ) → ( 𝜒 ∧ 𝜏 ) ) )