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Theorem e13 39292
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 39143 . 2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜓   )
3 e13.2 . 2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜏   )
4 e13.3 . 2 (𝜓 → (𝜏𝜂))
52, 3, 4e33 39278 1 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 39102  (   wvd3 39120
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 1056  df-vd1 39103  df-vd3 39123
This theorem is referenced by:  e13an  39293  en3lplem2VD  39393  rspsbc2VD  39404  ssralv2VD  39416  imbi12VD  39423  imbi13VD  39424  truniALTVD  39428
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