Theorem idn2 44603

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 44576	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜓   )

Syntax hints:  (   wvd2 44567

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 44568

This theorem is referenced by:  trsspwALT  44807  sspwtr  44810  pwtrVD  44813  pwtrrVD  44814  snssiALTVD  44816  sstrALT2VD  44823  suctrALT2VD  44825  elex2VD  44827  elex22VD  44828  eqsbc2VD  44829  tpid3gVD  44831  en3lplem1VD  44832  en3lplem2VD  44833  3ornot23VD  44836  orbi1rVD  44837  19.21a3con13vVD  44841  exbirVD  44842  exbiriVD  44843  rspsbc2VD  44844  tratrbVD  44850  syl5impVD  44852  ssralv2VD  44855  imbi12VD  44862  imbi13VD  44863  sbcim2gVD  44864  sbcbiVD  44865  truniALTVD  44867  trintALTVD  44869  onfrALTlem3VD  44876  onfrALTlem2VD  44878  onfrALTlem1VD  44879  relopabVD  44890  19.41rgVD  44891  hbimpgVD  44893  ax6e2eqVD  44896  ax6e2ndeqVD  44898  sb5ALTVD  44902  vk15.4jVD  44903  con3ALTVD  44905