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Theorem e123 38010
 Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e123.1 (   𝜑   ▶   𝜓   )
e123.2 (   𝜑   ,   𝜒   ▶   𝜃   )
e123.3 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜂   )
e123.4 (𝜓 → (𝜃 → (𝜂𝜁)))
Assertion
Ref Expression
e123 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜁   )

Proof of Theorem e123
StepHypRef Expression
1 e123.1 . . 3 (   𝜑   ▶   𝜓   )
21vd13 37847 . 2 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜓   )
3 e123.2 . . 3 (   𝜑   ,   𝜒   ▶   𝜃   )
43vd23 37848 . 2 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜃   )
5 e123.3 . 2 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜂   )
6 e123.4 . 2 (𝜓 → (𝜃 → (𝜂𝜁)))
72, 4, 5, 6e333 37981 1 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜁   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4  (   wvd1 37806  (   wvd2 37814  (   wvd3 37824 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 196  df-an 385  df-3an 1033  df-vd1 37807  df-vd2 37815  df-vd3 37827 This theorem is referenced by:  suctrALT2VD  38093
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