Theorem 3anim3i

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009)

	Ref	Expression
Hypothesis	3animi.1	⊢ ( 𝜑 → 𝜓 )
Assertion	3anim3i	⊢ ( ( 𝜒 ∧ 𝜃 ∧ 𝜑 ) → ( 𝜒 ∧ 𝜃 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		3animi.1	⊢ ( 𝜑 → 𝜓 )
2		id	⊢ ( 𝜒 → 𝜒 )
3		id	⊢ ( 𝜃 → 𝜃 )
4	2 3 1	3anim123i	⊢ ( ( 𝜒 ∧ 𝜃 ∧ 𝜑 ) → ( 𝜒 ∧ 𝜃 ∧ 𝜓 ) )