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Theorem e1a 38672
Description: A Virtual deduction elimination rule. syl 17 is e1a 38672 without virtual deductions. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e1a.1 (   𝜑   ▶   𝜓   )
e1a.2 (𝜓𝜒)
Assertion
Ref Expression
e1a (   𝜑   ▶   𝜒   )

Proof of Theorem e1a
StepHypRef Expression
1 e1a.1 . . . 4 (   𝜑   ▶   𝜓   )
21in1 38607 . . 3 (𝜑𝜓)
3 e1a.2 . . 3 (𝜓𝜒)
42, 3syl 17 . 2 (𝜑𝜒)
54dfvd1ir 38609 1 (   𝜑   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 38605
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 38606
This theorem is referenced by:  e1bi  38674  e1bir  38675  snelpwrVD  38886  unipwrVD  38887  sstrALT2VD  38889  elex2VD  38893  elex22VD  38894  eqsbc3rVD  38895  zfregs2VD  38896  tpid3gVD  38897  en3lplem1VD  38898  en3lpVD  38900  3ornot23VD  38902  3orbi123VD  38905  sbc3orgVD  38906  exbirVD  38908  3impexpVD  38911  3impexpbicomVD  38912  sbcoreleleqVD  38915  tratrbVD  38917  al2imVD  38918  syl5impVD  38919  ssralv2VD  38922  ordelordALTVD  38923  sbcim2gVD  38931  trsbcVD  38933  truniALTVD  38934  trintALTVD  38936  undif3VD  38938  sbcssgVD  38939  csbingVD  38940  onfrALTlem3VD  38943  simplbi2comtVD  38944  onfrALTlem2VD  38945  onfrALTVD  38947  csbeq2gVD  38948  csbsngVD  38949  csbxpgVD  38950  csbresgVD  38951  csbrngVD  38952  csbima12gALTVD  38953  csbunigVD  38954  csbfv12gALTVD  38955  con5VD  38956  relopabVD  38957  19.41rgVD  38958  2pm13.193VD  38959  hbimpgVD  38960  hbalgVD  38961  hbexgVD  38962  ax6e2eqVD  38963  ax6e2ndVD  38964  ax6e2ndeqVD  38965  2sb5ndVD  38966  2uasbanhVD  38967  e2ebindVD  38968  sb5ALTVD  38969  vk15.4jVD  38970  notnotrALTVD  38971  con3ALTVD  38972
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