ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.1 GIF version

Theorem pm5.1 533
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 ((𝜑𝜓) → (𝜑𝜓))

Proof of Theorem pm5.1
StepHypRef Expression
1 pm5.501 233 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21biimpa 280 1 ((𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.35  826  ssconb  3073
  Copyright terms: Public domain W3C validator