Theorem 3an6

Description: Analogue of an4 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Assertion	3an6	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ∧ ( 𝜏 ∧ 𝜂 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ∧ 𝜏 ) ∧ ( 𝜓 ∧ 𝜃 ∧ 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		an6	⊢ ( ( ( 𝜑 ∧ 𝜒 ∧ 𝜏 ) ∧ ( 𝜓 ∧ 𝜃 ∧ 𝜂 ) ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ∧ ( 𝜏 ∧ 𝜂 ) ) )
2	1	bicomi	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ∧ ( 𝜏 ∧ 𝜂 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ∧ 𝜏 ) ∧ ( 𝜓 ∧ 𝜃 ∧ 𝜂 ) ) )