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Theorem neeqtrri 2311
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 2119 . 2  |-  B  =  C
41, 3neeqtri 2309 1  |-  A  =/= 
C
Colors of variables: wff set class
Syntax hints:    = wceq 1314    =/= wne 2282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-4 1470  ax-17 1489  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2283
This theorem is referenced by:  pnfnemnf  7744  basendxnplusgndx  11908  plusgndxnmulrndx  11915  basendxnmulrndx  11916
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