MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  neeqtrri Unicode version

Theorem neeqtrri 2482
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 2300 . 2  |-  B  =  C
41, 3neeqtri 2480 1  |-  A  =/= 
C
Colors of variables: wff set class
Syntax hints:    = wceq 1632    =/= wne 2459
This theorem is referenced by:  cflim2  7905  pnfnemnf  10475  resslem  13217  zlmlem  16487  tnglem  18172  limsucncmpi  24956  matbas  27571  matplusg  27572  matvsca  27574
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-cleq 2289  df-ne 2461
  Copyright terms: Public domain W3C validator