Theorem idn2 44610

Description: Virtual deduction identity rule which is idd 24 with virtual deduction symbols. (Contributed by Alan Sare, 21-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
idn2	⊢ (   𝜑   ,   𝜓   ▶   𝜓   )

Proof of Theorem idn2

Step	Hyp	Ref	Expression
1		idd 24	. 2 ⊢ (𝜑 → (𝜓 → 𝜓))
2	1	dfvd2ir 44583	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜓   )

Syntax hints:  (   wvd2 44574

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 207  df-an 396  df-vd2 44575

This theorem is referenced by:  trsspwALT  44814  sspwtr  44817  pwtrVD  44820  pwtrrVD  44821  snssiALTVD  44823  sstrALT2VD  44830  suctrALT2VD  44832  elex2VD  44834  elex22VD  44835  eqsbc2VD  44836  tpid3gVD  44838  en3lplem1VD  44839  en3lplem2VD  44840  3ornot23VD  44843  orbi1rVD  44844  19.21a3con13vVD  44848  exbirVD  44849  exbiriVD  44850  rspsbc2VD  44851  tratrbVD  44857  syl5impVD  44859  ssralv2VD  44862  imbi12VD  44869  imbi13VD  44870  sbcim2gVD  44871  sbcbiVD  44872  truniALTVD  44874  trintALTVD  44876  onfrALTlem3VD  44883  onfrALTlem2VD  44885  onfrALTlem1VD  44886  relopabVD  44897  19.41rgVD  44898  hbimpgVD  44900  ax6e2eqVD  44903  ax6e2ndeqVD  44905  sb5ALTVD  44909  vk15.4jVD  44910  con3ALTVD  44912