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Theorem e33 41375
 Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e33.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e33.2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
e33.3 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
e33 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e33
StepHypRef Expression
1 e33.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e33.2 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
3 e33.3 . . 3 (𝜃 → (𝜏𝜂))
43a1i 11 . 2 (𝜃 → (𝜃 → (𝜏𝜂)))
51, 1, 2, 4e333 41374 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4  (   wvd3 41228 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 210  df-an 400  df-3an 1086  df-vd3 41231 This theorem is referenced by:  e33an  41376  e3  41378  e03  41381  e30  41385  e13  41389  e31  41392  e23  41396  e32  41399  truniALTVD  41519  trintALTVD  41521  onfrALTlem2VD  41530
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