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Theorem difeq1i 3397
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 3394 . 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 1649    \ cdif 3253
This theorem is referenced by:  difeq12i  3399  dfin3  3516  indif1  3521  indifcom  3522  difun1  3537  notab  3547  notrab  3554  undifabs  3641  difprsn1  3871  difprsn2  3872  orddif  4608  fresaun  5547  domunsncan  7137  phplem1  7215  elfiun  7363  axcclem  8263  dfn2  10159  restcld  17151  ufprim  17855  volun  19299  itgsplitioo  19589  uhgra0v  21205  usgra0v  21251  usgra1v  21268  cusgra3v  21332  ex-dif  21572  imadifxp  23874  braew  24380  coinflippvt  24514  ballotlemfval0  24525  wfi  25224  frind  25260  onint1  25906  itg2addnclem  25950  kelac2  26825  islinds2  26945  lindsind2  26951  mvdco  27050
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-rab 2651  df-dif 3259
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