ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  neeqtrri Unicode version

Theorem neeqtrri 2228
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
neeqtrr.1  =/=
neeqtrr.2  C
Assertion
Ref Expression
neeqtrri  =/=  C

Proof of Theorem neeqtrri
StepHypRef Expression
1 neeqtrr.1 . 2  =/=
2 neeqtrr.2 . . 3  C
32eqcomi 2041 . 2  C
41, 3neeqtri 2226 1  =/=  C
Colors of variables: wff set class
Syntax hints:   wceq 1242    =/= wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-ne 2203
This theorem is referenced by:  pnfnemnf  8467
  Copyright terms: Public domain W3C validator