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Theorem difeq12i 3472
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 3470 . 2  |-  ( A 
\  C )  =  ( B  \  C
)
3 difeq12i.2 . . 3  |-  C  =  D
43difeq2i 3471 . 2  |-  ( B 
\  C )  =  ( B  \  D
)
52, 4eqtri 2463 1  |-  ( A 
\  C )  =  ( B  \  D
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369    \ cdif 3325
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ral 2720  df-rab 2724  df-dif 3331
This theorem is referenced by:  difrab  3624  uniioombllem4  21066  zrdivrng  23919  gtiso  25996  preddif  27652  dvtanlem  28441  isdrngo1  28762  pwfi2f1o  29451
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