Theorem idn2 43462

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 43435	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜓   )

Syntax hints:  (   wvd2 43426

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 206  df-an 397  df-vd2 43427

This theorem is referenced by:  trsspwALT  43667  sspwtr  43670  pwtrVD  43673  pwtrrVD  43674  snssiALTVD  43676  sstrALT2VD  43683  suctrALT2VD  43685  elex2VD  43687  elex22VD  43688  eqsbc2VD  43689  tpid3gVD  43691  en3lplem1VD  43692  en3lplem2VD  43693  3ornot23VD  43696  orbi1rVD  43697  19.21a3con13vVD  43701  exbirVD  43702  exbiriVD  43703  rspsbc2VD  43704  tratrbVD  43710  syl5impVD  43712  ssralv2VD  43715  imbi12VD  43722  imbi13VD  43723  sbcim2gVD  43724  sbcbiVD  43725  truniALTVD  43727  trintALTVD  43729  onfrALTlem3VD  43736  onfrALTlem2VD  43738  onfrALTlem1VD  43739  relopabVD  43750  19.41rgVD  43751  hbimpgVD  43753  ax6e2eqVD  43756  ax6e2ndeqVD  43758  sb5ALTVD  43762  vk15.4jVD  43763  con3ALTVD  43765