Theorem idn3 38840

Description: Virtual deduction identity rule for three virtual hypotheses. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
idn3	|- (. ph ,. ps ,. ch ->. ch ).

Proof of Theorem idn3

Step	Hyp	Ref	Expression
1		idd 24	. . 3 |- ( ps -> ( ch -> ch ) )
2	1	a1i 11	. 2 |- ( ph -> ( ps -> ( ch -> ch ) ) )
3	2	dfvd3ir 38809	1 |- (. ph ,. ps ,. ch ->. ch ).

Syntax hints:   -> wi 4   (.wvd3 38803

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 197  df-an 386  df-3an 1039  df-vd3 38806

This theorem is referenced by:  suctrALT2VD  39071  en3lplem2VD  39079  exbirVD  39088  exbiriVD  39089  rspsbc2VD  39090  tratrbVD  39097  ssralv2VD  39102  imbi12VD  39109  imbi13VD  39110  truniALTVD  39114  trintALTVD  39116  onfrALTlem2VD  39125