Theorem ancomst 467

Description: Closed form of ancoms 461. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

Ref	Expression
ancomst	⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒))

Proof of Theorem ancomst

Step	Hyp	Ref	Expression
1		ancom 463	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑))
2	1	imbi1i 351	1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒))

Syntax hints:   → wi 4   ↔ wb 208   ∧ 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:  sbcom2  2200  ralcom  3284  ralcomf  3294  ovolgelb  25515  itg2leub  25769  nmoubi  30914  wl-sbcom2d  38012  ifpidg  44015  undmrnresiss  44128  ntrneiiso  44615  expcomdg  45024