Theorem e1a 38852

Description: A Virtual deduction elimination rule. syl 17 is e1a 38852 without virtual deductions. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e1a.1	|- (. ph ->. ps ).
e1a.2	|- ( ps -> ch )

Assertion

Ref	Expression
e1a	|- (. ph ->. ch ).

Proof of Theorem e1a

Step	Hyp	Ref	Expression
1		e1a.1	. . . 4 |- (. ph ->. ps ).
2	1	in1 38787	. . 3 |- ( ph -> ps )
3		e1a.2	. . 3 |- ( ps -> ch )
4	2, 3	syl 17	. 2 |- ( ph -> ch )
5	4	dfvd1ir 38789	1 |- (. ph ->. ch ).

Syntax hints:   -> wi 4   (.wvd1 38785

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-vd1 38786

This theorem is referenced by:  e1bi  38854  e1bir  38855  snelpwrVD  39066  unipwrVD  39067  sstrALT2VD  39069  elex2VD  39073  elex22VD  39074  eqsbc3rVD  39075  zfregs2VD  39076  tpid3gVD  39077  en3lplem1VD  39078  en3lpVD  39080  3ornot23VD  39082  3orbi123VD  39085  sbc3orgVD  39086  exbirVD  39088  3impexpVD  39091  3impexpbicomVD  39092  sbcoreleleqVD  39095  tratrbVD  39097  al2imVD  39098  syl5impVD  39099  ssralv2VD  39102  ordelordALTVD  39103  sbcim2gVD  39111  trsbcVD  39113  truniALTVD  39114  trintALTVD  39116  undif3VD  39118  sbcssgVD  39119  csbingVD  39120  onfrALTlem3VD  39123  simplbi2comtVD  39124  onfrALTlem2VD  39125  onfrALTVD  39127  csbeq2gVD  39128  csbsngVD  39129  csbxpgVD  39130  csbresgVD  39131  csbrngVD  39132  csbima12gALTVD  39133  csbunigVD  39134  csbfv12gALTVD  39135  con5VD  39136  relopabVD  39137  19.41rgVD  39138  2pm13.193VD  39139  hbimpgVD  39140  hbalgVD  39141  hbexgVD  39142  ax6e2eqVD  39143  ax6e2ndVD  39144  ax6e2ndeqVD  39145  2sb5ndVD  39146  2uasbanhVD  39147  e2ebindVD  39148  sb5ALTVD  39149  vk15.4jVD  39150  notnotrALTVD  39151  con3ALTVD  39152