Theorem bnj257

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

	Ref	Expression
Assertion	bnj257	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		ancom	⊢ ( ( 𝜒 ∧ 𝜃 ) ↔ ( 𝜃 ∧ 𝜒 ) )
2	1	anbi2i	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜃 ∧ 𝜒 ) ) )
3		bnj256	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) )
4		bnj256	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜃 ∧ 𝜒 ) ) )
5	2 3 4	3bitr4i	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒 ) )