ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  2th GIF version

Theorem 2th 163
Description: Two truths are equivalent. (Contributed by NM, 18-Aug-1993.)
Hypotheses
Ref Expression
2th.1 𝜑
2th.2 𝜓
Assertion
Ref Expression
2th (𝜑𝜓)

Proof of Theorem 2th
StepHypRef Expression
1 2th.2 . . 3 𝜓
21a1i 9 . 2 (𝜑𝜓)
3 2th.1 . . 3 𝜑
43a1i 9 . 2 (𝜓𝜑)
52, 4impbii 117 1 (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  trujust  1245  dftru2  1251  bitru  1255  vjust  2555  pwv  3575  int0  3625  0iin  3711  snnex  4152  ruv  4242  fo1st  5745  fo2nd  5746  eqer  6097  ener  6218  bdth  9786
  Copyright terms: Public domain W3C validator