Theorem an3 672

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 671	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ↔ ((𝜑 ∧ 𝜃) ∧ (𝜓 ∧ 𝜒)))
2	1	simplbi 502	1 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) → (𝜑 ∧ 𝜃))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  catideu  17756  usgredg2v  29614  trressn  39225  prtlem15  39690  clsk1indlem3  44810  poprelb  48314