ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  2th Structured version   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  1230  bitru  1238  vjust  2534  pwv  3531  int0  3581  0iin  3667  snnex  4104  ruv  4182  fo1st  5673  fo2nd  5674
  Copyright terms: Public domain W3C validator