Theorem an43 658

Description: Rearrangement of 4 conjuncts. (Contributed by Rodolfo Medina, 24-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)

Assertion

Ref	Expression
an43	⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ↔ ((𝜑 ∧ 𝜃) ∧ (𝜓 ∧ 𝜒)))

Proof of Theorem an43

Step	Hyp	Ref	Expression
1		an42 657	. 2 ⊢ (((𝜑 ∧ 𝜃) ∧ (𝜓 ∧ 𝜒)) ↔ ((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)))
2	1	bicomi 224	1 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ↔ ((𝜑 ∧ 𝜃) ∧ (𝜓 ∧ 𝜒)))

Syntax hints:   ↔ wb 206   ∧ 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 207  df-an 396

This theorem is referenced by:  an3  659  elfzuzb  13558  13an22anass  32483  bj-xpcossxp  37190  prtlem15  38876  an4com24  47280