Theorem idn2 45581

Description: Virtual deduction identity rule which is idd 25 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 25	. 2 ⊢ (𝜑 → (𝜓 → 𝜓))
2	1	dfvd2ir 45554	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜓   )

This proof depends on syntax axioms:  (   wvd2 45545

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-vd2 45546

This theorem is used by:  trsspwALT  45785  sspwtr  45788  pwtrVD  45791  pwtrrVD  45792  snssiALTVD  45794  sstrALT2VD  45801  suctrALT2VD  45803  elex2VD  45805  elex22VD  45806  eqsbc2VD  45807  tpid3gVD  45809  en3lplem1VD  45810  en3lplem2VD  45811  3ornot23VD  45814  orbi1rVD  45815  19.21a3con13vVD  45819  exbirVD  45820  exbiriVD  45821  rspsbc2VD  45822  tratrbVD  45828  syl5impVD  45830  ssralv2VD  45833  imbi12VD  45840  imbi13VD  45841  sbcim2gVD  45842  sbcbiVD  45843  truniALTVD  45845  trintALTVD  45847  onfrALTlem3VD  45854  onfrALTlem2VD  45856  onfrALTlem1VD  45857  relopabVD  45868  19.41rgVD  45869  hbimpgVD  45871  ax6e2eqVD  45874  ax6e2ndeqVD  45876  sb5ALTVD  45880  vk15.4jVD  45881  con3ALTVD  45883