Theorem neor 2885

Description: Logical OR with an equality. (Contributed by NM, 29-Apr-2007.)

Assertion

Ref	Expression
neor	|- ( ( A = B \/ ps ) <-> ( A =/= B -> ps ) )

Proof of Theorem neor

Step	Hyp	Ref	Expression
1		df-or 385	. 2 |- ( ( A = B \/ ps ) <-> ( -. A = B -> ps ) )
2		df-ne 2795	. . 3 |- ( A =/= B <-> -. A = B )
3	2	imbi1i 339	. 2 |- ( ( A =/= B -> ps ) <-> ( -. A = B -> ps ) )
4	1, 3	bitr4i 267	1 |- ( ( A = B \/ ps ) <-> ( A =/= B -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383   = wceq 1483   =/= wne 2794

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-ne 2795

This theorem is referenced by:  frsn  5189  ord0eln0  5779  fimaxre  10968  prime  11458  h1datomi  28440  elat2  29199  bnj563  30813  divrngidl  33827  dmncan1  33875  lkrshp4  34395  cvrcmp  34570  leat2  34581  isat3  34594  2llnmat  34810  2lnat  35070