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

Theorem ancrb 537
Description: Conjoin antecedent to right of consequent. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)
Assertion
Ref Expression
ancrb ((𝜑𝜓) ↔ (𝜑 → (𝜓𝜑)))

Proof of Theorem ancrb
StepHypRef Expression
1 iba 517 . 2 (𝜑 → (𝜓 ↔ (𝜓𝜑)))
21pm5.74i 260 1 ((𝜑𝜓) ↔ (𝜑 → (𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 382
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 197  df-an 383
This theorem is referenced by:  rababg  38405
  Copyright terms: Public domain W3C validator