Theorem idn2 36906

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	|- (. ph ,. ps ->. ps ).

Proof of Theorem idn2

Step	Hyp	Ref	Expression
1		idd 25	. 2 |- ( ph -> ( ps -> ps ) )
2	1	dfvd2ir 36870	1 |- (. ph ,. ps ->. ps ).

Syntax hints:   (.wvd2 36861

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 188  df-an 372  df-vd2 36862

This theorem is referenced by:  trsspwALT  37122  sspwtr  37125  pwtrVD  37136  pwtrrVD  37137  snssiALTVD  37139  sstrALT2VD  37146  suctrALT2VD  37148  elex2VD  37150  elex22VD  37151  eqsbc3rVD  37152  tpid3gVD  37154  en3lplem1VD  37155  en3lplem2VD  37156  3ornot23VD  37159  orbi1rVD  37160  19.21a3con13vVD  37164  exbirVD  37165  exbiriVD  37166  rspsbc2VD  37167  tratrbVD  37174  syl5impVD  37176  ssralv2VD  37179  imbi12VD  37186  imbi13VD  37187  sbcim2gVD  37188  sbcbiVD  37189  truniALTVD  37191  trintALTVD  37193  onfrALTlem3VD  37200  onfrALTlem2VD  37202  onfrALTlem1VD  37203  relopabVD  37214  19.41rgVD  37215  hbimpgVD  37217  ax6e2eqVD  37220  ax6e2ndeqVD  37222  sb5ALTVD  37226  vk15.4jVD  37227  con3ALTVD  37229