Theorem 3anrev

Description: Reversal law for triple conjunction. (Contributed by NM, 21-Apr-1994)

	Ref	Expression
Assertion	3anrev	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜒 ∧ 𝜓 ∧ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		3ancoma	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) )
2		3anrot	⊢ ( ( 𝜒 ∧ 𝜓 ∧ 𝜑 ) ↔ ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) )
3	1 2	bitr4i	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜒 ∧ 𝜓 ∧ 𝜑 ) )