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Theorem neeq12d 2613
Description: Deduction for inequality. (Contributed by NM, 24-Jul-2012.)
Hypotheses
Ref Expression
neeq1d.1  |-  ( ph  ->  A  =  B )
neeq12d.2  |-  ( ph  ->  C  =  D )
Assertion
Ref Expression
neeq12d  |-  ( ph  ->  ( A  =/=  C  <->  B  =/=  D ) )

Proof of Theorem neeq12d
StepHypRef Expression
1 neeq1d.1 . . 3  |-  ( ph  ->  A  =  B )
21neeq1d 2611 . 2  |-  ( ph  ->  ( A  =/=  C  <->  B  =/=  C ) )
3 neeq12d.2 . . 3  |-  ( ph  ->  C  =  D )
43neeq2d 2612 . 2  |-  ( ph  ->  ( B  =/=  C  <->  B  =/=  D ) )
52, 4bitrd 245 1  |-  ( ph  ->  ( A  =/=  C  <->  B  =/=  D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    = wceq 1652    =/= wne 2598
This theorem is referenced by:  3netr3d  2624  3netr4d  2625  infpssrlem4  8176  injresinjlem  11189  isnzr  16320  ptcmplem2  18074  usgrcyclnl1  21617  constr3lem6  21626  4cycl4dv4e  21645  derangsn  24846  derangenlem  24847  subfacp1lem3  24858  subfacp1lem5  24860  subfacp1lem6  24861  subfacp1  24862  sltval2  25576  sltres  25584  nodenselem3  25603  nodenselem5  25605  nodenselem7  25607  nofulllem4  25625  nofulllem5  25626  axlowdimlem6  25851  axlowdimlem14  25859  fvtransport  25931  fnelnfp  26692  stoweidlem43  27723  usg2wotspth  28268  2spontn0vne  28271  bnj1534  29125  bnj1542  29129  bnj1280  29290  cdlemkid3N  31631  cdlemkid4  31632
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-cleq 2428  df-ne 2600
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