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Theorem e123 41455
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 41294 . 2 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜓   )
3 e123.2 . . 3 (   𝜑   ,   𝜒   ▶   𝜃   )
43vd23 41295 . 2 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜃   )
5 e123.3 . 2 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜂   )
6 e123.4 . 2 (𝜓 → (𝜃 → (𝜂𝜁)))
72, 4, 5, 6e333 41426 1 (   𝜑   ,   𝜒   ,   𝜏   ▶   𝜁   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 41262  (   wvd2 41270  (   wvd3 41280
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-vd1 41263  df-vd2 41271  df-vd3 41283
This theorem is referenced by:  suctrALT2VD  41529
  Copyright terms: Public domain W3C validator