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Theorem eqnetrri 3014
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
eqnetrr.1 𝐴 = 𝐵
eqnetrr.2 𝐴𝐶
Assertion
Ref Expression
eqnetrri 𝐵𝐶

Proof of Theorem eqnetrri
StepHypRef Expression
1 eqnetrr.1 . . 3 𝐴 = 𝐵
21eqcomi 2780 . 2 𝐵 = 𝐴
3 eqnetrr.2 . 2 𝐴𝐶
42, 3eqnetri 3013 1 𝐵𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1631  wne 2943
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853  df-cleq 2764  df-ne 2944
This theorem is referenced by:  ballotlemii  30902  bj-2upln1upl  33340  wallispilem4  40798
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