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Theorem e13an 37997
 Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e13an.1 (   𝜑   ▶   𝜓   )
e13an.2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜏   )
e13an.3 ((𝜓𝜏) → 𝜂)
Assertion
Ref Expression
e13an (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e13an
StepHypRef Expression
1 e13an.1 . 2 (   𝜑   ▶   𝜓   )
2 e13an.2 . 2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜏   )
3 e13an.3 . . 3 ((𝜓𝜏) → 𝜂)
43ex 449 . 2 (𝜓 → (𝜏𝜂))
51, 2, 4e13 37996 1 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜂   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  (   wvd1 37806  (   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-vd3 37827 This theorem is referenced by: (None)
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