NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  neeqtrri GIF version

Theorem neeqtrri 2539
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 2357 . 2 B = C
41, 3neeqtri 2537 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: (None)
  Copyright terms: Public domain W3C validator