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Theorem difeq12i 3244
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 3242 . 2  |-  ( A 
\  C )  =  ( B  \  C
)
3 difeq12i.2 . . 3  |-  C  =  D
43difeq2i 3243 . 2  |-  ( B 
\  C )  =  ( B  \  D
)
52, 4eqtri 2192 1  |-  ( A 
\  C )  =  ( B  \  D
)
Colors of variables: wff set class
Syntax hints:    = wceq 1349    \ cdif 3119
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 610  ax-in2 611  ax-io 705  ax-5 1441  ax-7 1442  ax-gen 1443  ax-ie1 1487  ax-ie2 1488  ax-8 1498  ax-10 1499  ax-11 1500  ax-i12 1501  ax-bndl 1503  ax-4 1504  ax-17 1520  ax-i9 1524  ax-ial 1528  ax-i5r 1529  ax-ext 2153
This theorem depends on definitions:  df-bi 116  df-tru 1352  df-nf 1455  df-sb 1757  df-clab 2158  df-cleq 2164  df-clel 2167  df-nfc 2302  df-ral 2454  df-rab 2458  df-dif 3124
This theorem is referenced by:  difrab  3402  imadiflem  5279  imadif  5280
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