MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm5.1 Structured version   Unicode version

Theorem pm5.1 853
Description: Two propositions are equivalent if they are both true. Theorem *5.1 of [WhiteheadRussell] p. 123. (Contributed by NM, 21-May-1994.)
Assertion
Ref Expression
pm5.1  |-  ( (
ph  /\  ps )  ->  ( ph  <->  ps )
)

Proof of Theorem pm5.1
StepHypRef Expression
1 pm5.501 341 . 2  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
21biimpa 484 1  |-  ( (
ph  /\  ps )  ->  ( ph  <->  ps )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  pm5.35  894  ssconb  3600  raaan  3898  raaanv  3899  suppimacnvss  6813  mdsymi  25987  tsbi1  29112  abnotbtaxb  30098  raaan2  30167
  Copyright terms: Public domain W3C validator