Theorem bnj251

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Assertion	bnj251	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		bnj250	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ) )
2		anass	⊢ ( ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ↔ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) )
3	2	anbi2i	⊢ ( ( 𝜑 ∧ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) )
4	1 3	bitri	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) )