Theorem bnj312

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

	Ref	Expression
Assertion	bnj312	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜓 ∧ 𝜑 ∧ 𝜒 ∧ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		3ancoma	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) )
2	1	anbi1i	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ↔ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) )
3		df-bnj17	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) )
4		df-bnj17	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) )
5	2 3 4	3bitr4i	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜓 ∧ 𝜑 ∧ 𝜒 ∧ 𝜃 ) )