Theorem an31

Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012) (Proof shortened by Wolf Lammen, 31-Dec-2012)

	Ref	Expression
Assertion	an31	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( ( 𝜒 ∧ 𝜓 ) ∧ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		an13	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ↔ ( 𝜒 ∧ ( 𝜓 ∧ 𝜑 ) ) )
2		anass	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) )
3		anass	⊢ ( ( ( 𝜒 ∧ 𝜓 ) ∧ 𝜑 ) ↔ ( 𝜒 ∧ ( 𝜓 ∧ 𝜑 ) ) )
4	1 2 3	3bitr4i	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( ( 𝜒 ∧ 𝜓 ) ∧ 𝜑 ) )