Theorem anim1d

Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994)

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

Proof

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