Theorem idn2 45040

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 45013	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜓   )

Syntax hints:  (   wvd2 45004

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 45005

This theorem is referenced by:  trsspwALT  45244  sspwtr  45247  pwtrVD  45250  pwtrrVD  45251  snssiALTVD  45253  sstrALT2VD  45260  suctrALT2VD  45262  elex2VD  45264  elex22VD  45265  eqsbc2VD  45266  tpid3gVD  45268  en3lplem1VD  45269  en3lplem2VD  45270  3ornot23VD  45273  orbi1rVD  45274  19.21a3con13vVD  45278  exbirVD  45279  exbiriVD  45280  rspsbc2VD  45281  tratrbVD  45287  syl5impVD  45289  ssralv2VD  45292  imbi12VD  45299  imbi13VD  45300  sbcim2gVD  45301  sbcbiVD  45302  truniALTVD  45304  trintALTVD  45306  onfrALTlem3VD  45313  onfrALTlem2VD  45315  onfrALTlem1VD  45316  relopabVD  45327  19.41rgVD  45328  hbimpgVD  45330  ax6e2eqVD  45333  ax6e2ndeqVD  45335  sb5ALTVD  45339  vk15.4jVD  45340  con3ALTVD  45342