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Theorem e13 39496
 Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e13.1 (   𝜑   ▶   𝜓   )
e13.2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜏   )
e13.3 (𝜓 → (𝜏𝜂))
Assertion
Ref Expression
e13 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e13
StepHypRef Expression
1 e13.1 . . 3 (   𝜑   ▶   𝜓   )
21vd13 39347 . 2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜓   )
3 e13.2 . 2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜏   )
4 e13.3 . 2 (𝜓 → (𝜏𝜂))
52, 3, 4e33 39482 1 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜂   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4  (   wvd1 39306  (   wvd3 39324 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 385  df-3an 1074  df-vd1 39307  df-vd3 39327 This theorem is referenced by:  e13an  39497  en3lplem2VD  39597  rspsbc2VD  39608  ssralv2VD  39620  imbi12VD  39627  imbi13VD  39628  truniALTVD  39632
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