Theorem an13 643

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 640	. 2 ⊢ (((𝜓 ∧ 𝜑) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒)))
2		ancom 460	. 2 ⊢ (((𝜓 ∧ 𝜑) ∧ 𝜒) ↔ (𝜒 ∧ (𝜓 ∧ 𝜑)))
3	1, 2	bitr3i 276	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) ↔ (𝜒 ∧ (𝜓 ∧ 𝜑)))

Syntax hints:   ↔ wb 205   ∧ wa 395

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 206  df-an 396

This theorem is referenced by:  an31  644  elsnxp  6183  dchrelbas3  26291  dfiota3  34152  bj-dfmpoa  35216  islpln5  37476  islvol5  37520  dibelval3  39088  opeliun2xp  45556