MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  imbi1 Structured version   Visualization version   GIF version

Theorem imbi1 346
Description: Theorem *4.84 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
imbi1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))

Proof of Theorem imbi1
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
21imbi1d 340 1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205
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
This theorem is referenced by:  imbi1i  348  nanbi1  1495  ifpbi1  43144  3impexpVD  44532  ancomstVD  44541  onfrALTVD  44567  hbimpgVD  44580  hbexgVD  44582  ax6e2ndeqVD  44585  ax6e2ndeqALT  44607
  Copyright terms: Public domain W3C validator