Theorem 3ancomb 970

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

Assertion

Ref	Expression
3ancomb	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜑 ∧ 𝜒 ∧ 𝜓))

Proof of Theorem 3ancomb

Step	Hyp	Ref	Expression
1		3ancoma 969	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
2		3anrot 967	. 2 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) ↔ (𝜑 ∧ 𝜒 ∧ 𝜓))
3	1, 2	bitri 183	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜑 ∧ 𝜒 ∧ 𝜓))

Syntax hints:   ↔ wb 104   ∧ w3a 962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 964

This theorem is referenced by:  3simpb  979  addcanprg  7424  elioore  9695  xmetrtri  12545