Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e1bi Structured version   Visualization version   GIF version

Theorem e1bi 41273
Description: Biconditional form of e1a 41271. sylib 221 is e1bi 41273 without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e1bi.1 (   𝜑   ▶   𝜓   )
e1bi.2 (𝜓𝜒)
Assertion
Ref Expression
e1bi (   𝜑   ▶   𝜒   )

Proof of Theorem e1bi
StepHypRef Expression
1 e1bi.1 . 2 (   𝜑   ▶   𝜓   )
2 e1bi.2 . . 3 (𝜓𝜒)
32biimpi 219 . 2 (𝜓𝜒)
41, 3e1a 41271 1 (   𝜑   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wb 209  (   wvd1 41213
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 210  df-vd1 41214
This theorem is referenced by:  zfregs2VD  41485  tpid3gVD  41486  en3lplem2VD  41488  ordelordALTVD  41511
  Copyright terms: Public domain W3C validator