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Theorem eqnetri 2533
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
eqnetr.1 A = B
eqnetr.2 BC
Assertion
Ref Expression
eqnetri AC

Proof of Theorem eqnetri
StepHypRef Expression
1 eqnetr.2 . 2 BC
2 eqnetr.1 . . 3 A = B
32neeq1i 2526 . 2 (ACBC)
41, 3mpbir 200 1 AC
Colors of variables: wff setvar class
Syntax hints:   = wceq 1642  wne 2516
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346  df-ne 2518
This theorem is referenced by:  eqnetrri  2535  tfin1c  4499  map0  6025  ce0nnulb  6182  addceq0  6219  nchoicelem14  6302
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