Theorem anim2d

Description: Add a conjunct to left of antecedent and consequent in a deduction. (Contributed by NM, 14-May-1993)

	Ref	Expression
Hypothesis	anim1d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	anim2d	⊢ ( 𝜑 → ( ( 𝜃 ∧ 𝜓 ) → ( 𝜃 ∧ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		anim1d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		idd	⊢ ( 𝜑 → ( 𝜃 → 𝜃 ) )
3	2 1	anim12d	⊢ ( 𝜑 → ( ( 𝜃 ∧ 𝜓 ) → ( 𝜃 ∧ 𝜒 ) ) )