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Theorem neeqtrri 2747
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
neeqtrr.1  |-  A  =/= 
B
neeqtrr.2  |-  C  =  B
Assertion
Ref Expression
neeqtrri  |-  A  =/= 
C

Proof of Theorem neeqtrri
StepHypRef Expression
1 neeqtrr.1 . 2  |-  A  =/= 
B
2 neeqtrr.2 . . 3  |-  C  =  B
32eqcomi 2464 . 2  |-  B  =  C
41, 3neeqtri 2746 1  |-  A  =/= 
C
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370    =/= wne 2644
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-cleq 2443  df-ne 2646
This theorem is referenced by:  cflim2  8535  pnfnemnf  11200  resslem  14335  zlmlem  18059  matbas  18425  matplusg  18426  matvsca  18428  tnglem  20344  resvlem  26435  limsucncmpi  28427
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