Theorem 3impdir

Description: Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995)

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

Proof

Step	Hyp	Ref	Expression
1		3impdir.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜓 ) ) → 𝜃 )
2	1	anandirs	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜓 ) → 𝜃 )
3	2	3impa	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) → 𝜃 )