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Theorem e233 39309
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 29-Feb-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e233.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e233.2 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜏   )
e233.3 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜂   )
e233.4 (𝜒 → (𝜏 → (𝜂𝜁)))
Assertion
Ref Expression
e233 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜁   )

Proof of Theorem e233
StepHypRef Expression
1 e233.1 . . . 4 (   𝜑   ,   𝜓   ▶   𝜒   )
21dfvd2i 39118 . . 3 (𝜑 → (𝜓𝜒))
3 e233.2 . . . 4 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜏   )
43dfvd3i 39125 . . 3 (𝜑 → (𝜓 → (𝜃𝜏)))
5 e233.3 . . . 4 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜂   )
65dfvd3i 39125 . . 3 (𝜑 → (𝜓 → (𝜃𝜂)))
7 e233.4 . . 3 (𝜒 → (𝜏 → (𝜂𝜁)))
82, 4, 6, 7ee233 39042 . 2 (𝜑 → (𝜓 → (𝜃𝜁)))
98dfvd3ir 39126 1 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜁   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 39110  (   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-vd2 39111  df-vd3 39123
This theorem is referenced by:  truniALTVD  39428  onfrALTlem2VD  39439
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