Theorem anim1i

Description: Introduce conjunct to both sides of an implication. (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Hypothesis	anim1i.1	⊢ ( 𝜑 → 𝜓 )
Assertion	anim1i	⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		anim1i.1	⊢ ( 𝜑 → 𝜓 )
2		id	⊢ ( 𝜒 → 𝜒 )
3	1 2	anim12i	⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) )