MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  neeq2OLD Structured version   Unicode version

Theorem neeq2OLD 2715
Description: Obsolete proof of neeq2 2714 as of 18-Nov-2019. (Contributed by NM, 19-Nov-1994.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
neeq2OLD  |-  ( A  =  B  ->  ( C  =/=  A  <->  C  =/=  B ) )

Proof of Theorem neeq2OLD
StepHypRef Expression
1 eqeq2 2444 . . 3  |-  ( A  =  B  ->  ( C  =  A  <->  C  =  B ) )
21notbid 295 . 2  |-  ( A  =  B  ->  ( -.  C  =  A  <->  -.  C  =  B ) )
3 df-ne 2627 . 2  |-  ( C  =/=  A  <->  -.  C  =  A )
4 df-ne 2627 . 2  |-  ( C  =/=  B  <->  -.  C  =  B )
52, 3, 43bitr4g 291 1  |-  ( A  =  B  ->  ( C  =/=  A  <->  C  =/=  B ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    = wceq 1437    =/= wne 2625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-cleq 2421  df-ne 2627
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator