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Theorem difeq12i 3558
Description: Equality inference for class difference. (Contributed by NM, 29-Aug-2004.)
Hypotheses
Ref Expression
difeq1i.1  |-  A  =  B
difeq12i.2  |-  C  =  D
Assertion
Ref Expression
difeq12i  |-  ( A 
\  C )  =  ( B  \  D
)

Proof of Theorem difeq12i
StepHypRef Expression
1 difeq1i.1 . . 3  |-  A  =  B
21difeq1i 3556 . 2  |-  ( A 
\  C )  =  ( B  \  C
)
3 difeq12i.2 . . 3  |-  C  =  D
43difeq2i 3557 . 2  |-  ( B 
\  C )  =  ( B  \  D
)
52, 4eqtri 2431 1  |-  ( A 
\  C )  =  ( B  \  D
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1405    \ cdif 3410
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758  df-rab 2762  df-dif 3416
This theorem is referenced by:  difrab  3723  uniioombllem4  22179  zrdivrng  25728  gtiso  27843  mthmpps  29675  preddif  29944  dvtanlemOLD  31418  isdrngo1  31622  pwfi2f1o  35387  pwfi2f1oOLD  35388
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