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Theorem e21 39274
Description: A virtual deduction elimination rule (see syl6ci 71). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e21.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e21.2 (   𝜑   ▶   𝜃   )
e21.3 (𝜒 → (𝜃𝜏))
Assertion
Ref Expression
e21 (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e21
StepHypRef Expression
1 e21.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e21.2 . . 3 (   𝜑   ▶   𝜃   )
32vd12 39142 . 2 (   𝜑   ,   𝜓   ▶   𝜃   )
4 e21.3 . 2 (𝜒 → (𝜃𝜏))
51, 3, 4e22 39213 1 (   𝜑   ,   𝜓   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 39102  (   wvd2 39110
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 197  df-an 385  df-vd1 39103  df-vd2 39111
This theorem is referenced by:  e21an  39275  en3lplem1VD  39392  exbiriVD  39403  syl5impVD  39413  sbcim2gVD  39425  onfrALTlem3VD  39437  onfrALTlem2VD  39439  hbimpgVD  39454  ax6e2eqVD  39457  vk15.4jVD  39464
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