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

Theorem neeqtrri 2626
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 2442 . 2  |-  B  =  C
41, 3neeqtri 2624 1  |-  A  =/= 
C
Colors of variables: wff set class
Syntax hints:    = wceq 1653    =/= wne 2601
This theorem is referenced by:  cflim2  8145  pnfnemnf  10719  resslem  13524  zlmlem  16800  tnglem  18683  limsucncmpi  26197  matbas  27447  matplusg  27448  matvsca  27450
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-cleq 2431  df-ne 2603
  Copyright terms: Public domain W3C validator