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Theorem e2bir 39360
 Description: Right biconditional form of e2 39358. syl6ibr 242 is e2bir 39360 without virtual deductions. (Contributed by Alan Sare, 29-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e2bir.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e2bir.2 (𝜃𝜒)
Assertion
Ref Expression
e2bir (   𝜑   ,   𝜓   ▶   𝜃   )

Proof of Theorem e2bir
StepHypRef Expression
1 e2bir.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e2bir.2 . . 3 (𝜃𝜒)
32biimpri 218 . 2 (𝜒𝜃)
41, 3e2 39358 1 (   𝜑   ,   𝜓   ▶   𝜃   )
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196  (   wvd2 39295 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-vd2 39296 This theorem is referenced by:  trsspwALT  39547  pwtrVD  39558  eqsbc3rVD  39574  tpid3gVD  39576  onfrALTlem1VD  39625
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