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Theorem difeq1i 3453
Description: Inference adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002.)
Hypothesis
Ref Expression
difeq1i.1  |-  A  =  B
Assertion
Ref Expression
difeq1i  |-  ( A 
\  C )  =  ( B  \  C
)

Proof of Theorem difeq1i
StepHypRef Expression
1 difeq1i.1 . 2  |-  A  =  B
2 difeq1 3450 . 2  |-  ( A  =  B  ->  ( A  \  C )  =  ( B  \  C
) )
31, 2ax-mp 8 1  |-  ( A 
\  C )  =  ( B  \  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1652    \ cdif 3309
This theorem is referenced by:  difeq12i  3455  dfin3  3572  indif1  3577  indifcom  3578  difun1  3593  notab  3603  notrab  3610  undifabs  3697  difprsn1  3927  difprsn2  3928  orddif  4667  fresaun  5606  domunsncan  7200  phplem1  7278  elfiun  7427  axcclem  8329  dfn2  10226  restcld  17228  bwth  17465  ufprim  17933  volun  19431  itgsplitioo  19721  uhgra0v  21337  usgra0v  21383  usgra1v  21401  cusgra3v  21465  ex-dif  21723  imadifxp  24030  braew  24585  coinflippvt  24734  ballotlemfval0  24745  wfi  25474  frind  25510  onint1  26191  itg2addnclem  26246  kelac2  27131  islinds2  27251  lindsind2  27257  mvdco  27356  f12dfv  28066  f13dfv  28067
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-dif 3315
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