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Theorem difeq12i 3549
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 3547 . 2  |-  ( A 
\  C )  =  ( B  \  C
)
3 difeq12i.2 . . 3  |-  C  =  D
43difeq2i 3548 . 2  |-  ( B 
\  C )  =  ( B  \  D
)
52, 4eqtri 2473 1  |-  ( A 
\  C )  =  ( B  \  D
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1444    \ cdif 3401
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431
This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rab 2746  df-dif 3407
This theorem is referenced by:  difrab  3717  preddif  5405  uniioombllem4  22544  zrdivrng  26160  gtiso  28281  mthmpps  30220  dvtanlemOLD  31991  isdrngo1  32195  pwfi2f1o  35954  salexct2  38198
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