Theorem an13 657

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

Assertion

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

Proof of Theorem an13

Step	Hyp	Ref	Expression
1		an21 654	. 2 ⊢ (((𝜓 ∧ 𝜑) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒)))
2		ancom 464	. 2 ⊢ (((𝜓 ∧ 𝜑) ∧ 𝜒) ↔ (𝜒 ∧ (𝜓 ∧ 𝜑)))
3	1, 2	bitr3i 279	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) ↔ (𝜒 ∧ (𝜓 ∧ 𝜑)))

Syntax hints:   ↔ wb 208   ∧ wa 399

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209  df-an 400

This theorem is referenced by:  an31  658  opeliun2xp  5711  elsnxp  6273  dchrelbas3  27290  dfiota3  36232  bj-dfmpoa  37569  islpln5  40120  islvol5  40164  dibelval3  41732