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Theorem e3bi 41063
Description: Biconditional form of e3 41062. syl8ib 258 is e3bi 41063 without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e3bi.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e3bi.2 (𝜃𝜏)
Assertion
Ref Expression
e3bi (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e3bi
StepHypRef Expression
1 e3bi.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e3bi.2 . . 3 (𝜃𝜏)
32biimpi 218 . 2 (𝜃𝜏)
41, 3e3 41062 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wb 208  (   wvd3 40912
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 209  df-an 399  df-3an 1084  df-vd3 40915
This theorem is referenced by:  en3lplem2VD  41169
  Copyright terms: Public domain W3C validator