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Theorem neeqtrri 2386
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 2191 . 2  |-  B  =  C
41, 3neeqtri 2384 1  |-  A  =/= 
C
Colors of variables: wff set class
Syntax hints:    = wceq 1363    =/= wne 2357
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1457  ax-gen 1459  ax-4 1520  ax-17 1536  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-cleq 2180  df-ne 2358
This theorem is referenced by:  pnfnemnf  8025  basendxnplusgndx  12597  plusgndxnmulrndx  12605  basendxnmulrndx  12606
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