Theorem an13 646

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 643	. 2 ⊢ (((𝜓 ∧ 𝜑) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒)))
2		ancom 464	. 2 ⊢ (((𝜓 ∧ 𝜑) ∧ 𝜒) ↔ (𝜒 ∧ (𝜓 ∧ 𝜑)))
3	1, 2	bitr3i 280	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) ↔ (𝜒 ∧ (𝜓 ∧ 𝜑)))

Syntax hints:   ↔ wb 209   ∧ 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 210  df-an 400

This theorem is referenced by:  an31  647  elsnxp  6110  dchrelbas3  25822  dfiota3  33497  bj-dfmpoa  34533  islpln5  36831  islvol5  36875  dibelval3  38443  opeliun2xp  44734