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Theorem difeq12i 3266
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 3264 . 2  |-  ( A 
\  C )  =  ( B  \  C
)
3 difeq12i.2 . . 3  |-  C  =  D
43difeq2i 3265 . 2  |-  ( B 
\  C )  =  ( B  \  D
)
52, 4eqtri 2210 1  |-  ( A 
\  C )  =  ( B  \  D
)
Colors of variables: wff set class
Syntax hints:    = wceq 1364    \ cdif 3141
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rab 2477  df-dif 3146
This theorem is referenced by:  difrab  3424  imadiflem  5314  imadif  5315
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