Theorem 3impdi

Description: Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995)

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

Proof

Step	Hyp	Ref	Expression
1		3impdi.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜑 ∧ 𝜒 ) ) → 𝜃 )
2	1	anandis	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
3	2	3impb	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )