MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  bicom1 Structured version   Visualization version   GIF version

Theorem bicom1 213
Description: Commutative law for the biconditional. (Contributed by Wolf Lammen, 10-Nov-2012.)
Assertion
Ref Expression
bicom1 ((𝜑𝜓) → (𝜓𝜑))

Proof of Theorem bicom1
StepHypRef Expression
1 biimpr 212 . 2 ((𝜑𝜓) → (𝜓𝜑))
2 biimp 207 . 2 ((𝜑𝜓) → (𝜑𝜓))
31, 2impbid 204 1 ((𝜑𝜓) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198
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 199
This theorem is referenced by:  bicom  214  bicomi  216  con3ALTOLD  1069  nanass  1580  nanassOLD  1581  frege55aid  39115  frege55lem2a  39117  bisaiaisb  42007  confun4  42036  confun5  42037
  Copyright terms: Public domain W3C validator