Theorem idn2 45057

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 45030	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜓   )

Syntax hints:  (   wvd2 45021

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 208  df-an 397  df-vd2 45022

This theorem is referenced by:  trsspwALT  45261  sspwtr  45264  pwtrVD  45267  pwtrrVD  45268  snssiALTVD  45270  sstrALT2VD  45277  suctrALT2VD  45279  elex2VD  45281  elex22VD  45282  eqsbc2VD  45283  tpid3gVD  45285  en3lplem1VD  45286  en3lplem2VD  45287  3ornot23VD  45290  orbi1rVD  45291  19.21a3con13vVD  45295  exbirVD  45296  exbiriVD  45297  rspsbc2VD  45298  tratrbVD  45304  syl5impVD  45306  ssralv2VD  45309  imbi12VD  45316  imbi13VD  45317  sbcim2gVD  45318  sbcbiVD  45319  truniALTVD  45321  trintALTVD  45323  onfrALTlem3VD  45330  onfrALTlem2VD  45332  onfrALTlem1VD  45333  relopabVD  45344  19.41rgVD  45345  hbimpgVD  45347  ax6e2eqVD  45350  ax6e2ndeqVD  45352  sb5ALTVD  45356  vk15.4jVD  45357  con3ALTVD  45359