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Theorem e101 40889
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e101.1 (   𝜑   ▶   𝜓   )
e101.2 𝜒
e101.3 (   𝜑   ▶   𝜃   )
e101.4 (𝜓 → (𝜒 → (𝜃𝜏)))
Assertion
Ref Expression
e101 (   𝜑   ▶   𝜏   )

Proof of Theorem e101
StepHypRef Expression
1 e101.1 . 2 (   𝜑   ▶   𝜓   )
2 e101.2 . . 3 𝜒
32vd01 40808 . 2 (   𝜑   ▶   𝜒   )
4 e101.3 . 2 (   𝜑   ▶   𝜃   )
5 e101.4 . 2 (𝜓 → (𝜒 → (𝜃𝜏)))
61, 3, 4, 5e111 40885 1 (   𝜑   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 40780
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 208  df-vd1 40781
This theorem is referenced by:  sbcoreleleqVD  41070
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