Theorem an3 657

Description: A rearrangement of conjuncts. (Contributed by Rodolfo Medina, 25-Sep-2010.)

Assertion

Ref	Expression
an3	⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) → (𝜑 ∧ 𝜃))

Proof of Theorem an3

Step	Hyp	Ref	Expression
1		an43 656	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ↔ ((𝜑 ∧ 𝜃) ∧ (𝜓 ∧ 𝜒)))
2	1	simplbi 500	1 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) → (𝜑 ∧ 𝜃))

Syntax hints:   → wi 4   ∧ wa 398

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 399

This theorem is referenced by:  catideu  16940  usgredg2v  27003  prtlem15  36005  clsk1indlem3  40386  poprelb  43679