Theorem bnj290

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

	Ref	Expression
Assertion	bnj290	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		3anrot	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜒 ∧ 𝜃 ∧ 𝜓 ) )
2	1	anbi2i	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) ↔ ( 𝜑 ∧ ( 𝜒 ∧ 𝜃 ∧ 𝜓 ) ) )
3		bnj252	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) )
4		bnj252	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) ↔ ( 𝜑 ∧ ( 𝜒 ∧ 𝜃 ∧ 𝜓 ) ) )
5	2 3 4	3bitr4i	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) )