MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ancomst Structured version   Visualization version   GIF version

Theorem ancomst 464
Description: Closed form of ancoms 458. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
ancomst (((𝜑𝜓) → 𝜒) ↔ ((𝜓𝜑) → 𝜒))

Proof of Theorem ancomst
StepHypRef Expression
1 ancom 460 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
21imbi1i 349 1 (((𝜑𝜓) → 𝜒) ↔ ((𝜓𝜑) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  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:  sbcom2  2153  ralcom  3280  ralcomf  3293  ovolgelb  25360  itg2leub  25615  nmoubi  30530  wl-sbcom2d  36936  ifpidg  42799  undmrnresiss  42912  ntrneiiso  43399  expcomdg  43818
  Copyright terms: Public domain W3C validator