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Theorem neeqtrri 2469
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 2287 . 2  |-  B  =  C
41, 3neeqtri 2467 1  |-  A  =/= 
C
Colors of variables: wff set class
Syntax hints:    = wceq 1623    =/= wne 2446
This theorem is referenced by:  cflim2  7889  pnfnemnf  10459  resslem  13201  zlmlem  16471  tnglem  18156  limsucncmpi  24884  matbas  27468  matplusg  27469  matvsca  27471
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-cleq 2276  df-ne 2448
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