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Theorem neeqtrri 2314
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
neeqtrr.1 𝐴𝐵
neeqtrr.2 𝐶 = 𝐵
Assertion
Ref Expression
neeqtrri 𝐴𝐶

Proof of Theorem neeqtrri
StepHypRef Expression
1 neeqtrr.1 . 2 𝐴𝐵
2 neeqtrr.2 . . 3 𝐶 = 𝐵
32eqcomi 2121 . 2 𝐵 = 𝐶
41, 3neeqtri 2312 1 𝐴𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1316  wne 2285
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-5 1408  ax-gen 1410  ax-4 1472  ax-17 1491  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-cleq 2110  df-ne 2286
This theorem is referenced by:  pnfnemnf  7788  basendxnplusgndx  11992  plusgndxnmulrndx  11999  basendxnmulrndx  12000
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