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Theorem e01 38736
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e01.1 𝜑
e01.2 (   𝜓   ▶   𝜒   )
e01.3 (𝜑 → (𝜒𝜃))
Assertion
Ref Expression
e01 (   𝜓   ▶   𝜃   )

Proof of Theorem e01
StepHypRef Expression
1 e01.1 . . 3 𝜑
21vd01 38642 . 2 (   𝜓   ▶   𝜑   )
3 e01.2 . 2 (   𝜓   ▶   𝜒   )
4 e01.3 . 2 (𝜑 → (𝜒𝜃))
52, 3, 4e11 38733 1 (   𝜓   ▶   𝜃   )
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:  e01an  38737  trsspwALT  38865  sspwtr  38868  pwtrVD  38879  pwtrrVD  38880  snssiALTVD  38882  snelpwrVD  38886  sstrALT2VD  38889  suctrALT2VD  38891  3impexpVD  38911  ax6e2eqVD  38963  ax6e2ndVD  38964  2sb5ndVD  38966  vk15.4jVD  38970
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