Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj887 Unicode version

Theorem bnj887 32601
Description: /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj887.1 No typesetting for: |- ( ph <-> ph' )
bnj887.2 No typesetting for: |- ( ps <-> ps' )
bnj887.3 No typesetting for: |- ( ch <-> ch' )
bnj887.4 No typesetting for: |- ( th <-> th' )
Assertion
Ref Expression
bnj887 No typesetting for: |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph' /\ ps' /\ ch' /\ th' ) )

Proof of Theorem bnj887
StepHypRef Expression
1 bnj887.1 . . . 4 No typesetting for: |- ( ph <-> ph' )
2 bnj887.2 . . . 4 No typesetting for: |- ( ps <-> ps' )
3 bnj887.3 . . . 4 No typesetting for: |- ( ch <-> ch' )
41, 2, 33anbi123i 1177 . . 3 No typesetting for: |- ( ( ph /\ ps /\ ch ) <-> ( ph' /\ ps' /\ ch' ) )
5 bnj887.4 . . 3 No typesetting for: |- ( th <-> th' )
64, 5anbi12i 697 . 2 No typesetting for: |- ( ( ( ph /\ ps /\ ch ) /\ th ) <-> ( ( ph' /\ ps' /\ ch' ) /\ th' ) )
7 df-bnj17 32518 . 2
8 df-bnj17 32518 . 2 No typesetting for: |- ( ( ph' /\ ps' /\ ch' /\ th' ) <-> ( ( ph' /\ ps' /\ ch' ) /\ th' ) )
96, 7, 83bitr4i 277 1 No typesetting for: |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph' /\ ps' /\ ch' /\ th' ) )
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  /\w3a 965  /\w-bnj17 32517
This theorem is referenced by:  bnj1040  32806  bnj1128  32824
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 185  df-an 371  df-3an 967  df-bnj17 32518
  Copyright terms: Public domain W3C validator