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

Theorem eqnetrrd 2225
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
eqnetrrd.1 (φA = B)
eqnetrrd.2 (φA𝐶)
Assertion
Ref Expression
eqnetrrd (φB𝐶)

Proof of Theorem eqnetrrd
StepHypRef Expression
1 eqnetrrd.1 . . 3 (φA = B)
21eqcomd 2042 . 2 (φB = A)
3 eqnetrrd.2 . 2 (φA𝐶)
42, 3eqnetrd 2223 1 (φB𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = 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: (None)
  Copyright terms: Public domain W3C validator