Theorem an13

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

	Ref	Expression
Assertion	an13	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ↔ ( 𝜒 ∧ ( 𝜓 ∧ 𝜑 ) ) )

Proof

Step	Hyp	Ref	Expression
1		an21	⊢ ( ( ( 𝜓 ∧ 𝜑 ) ∧ 𝜒 ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) )
2		ancom	⊢ ( ( ( 𝜓 ∧ 𝜑 ) ∧ 𝜒 ) ↔ ( 𝜒 ∧ ( 𝜓 ∧ 𝜑 ) ) )
3	1 2	bitr3i	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ↔ ( 𝜒 ∧ ( 𝜓 ∧ 𝜑 ) ) )