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Theorem e021 37911
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e021.1 𝜑
e021.2 (   𝜓   ,   𝜒   ▶   𝜃   )
e021.3 (   𝜓   ▶   𝜏   )
e021.4 (𝜑 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e021 (   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e021
StepHypRef Expression
1 e021.1 . . 3 𝜑
21vd01 37843 . 2 (   𝜓   ▶   𝜑   )
3 e021.2 . 2 (   𝜓   ,   𝜒   ▶   𝜃   )
4 e021.3 . 2 (   𝜓   ▶   𝜏   )
5 e021.4 . 2 (𝜑 → (𝜃 → (𝜏𝜂)))
62, 3, 4, 5e121 37902 1 (   𝜓   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 37806  (   wvd2 37814
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-vd1 37807  df-vd2 37815
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator