Theorem bnj432

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

	Ref	Expression
Assertion	bnj432	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜒 ∧ 𝜃 ) ∧ ( 𝜑 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		bnj422	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓 ) )
2		bnj256	⊢ ( ( 𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓 ) ↔ ( ( 𝜒 ∧ 𝜃 ) ∧ ( 𝜑 ∧ 𝜓 ) ) )
3	1 2	bitri	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜒 ∧ 𝜃 ) ∧ ( 𝜑 ∧ 𝜓 ) ) )