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Theorem difeq2i 3113
Description: Inference adding difference to the left in a class equality. (Contributed by NM, 15-Nov-2002.)
Hypothesis
Ref Expression
difeq1i.1  |-  A  =  B
Assertion
Ref Expression
difeq2i  |-  ( C 
\  A )  =  ( C  \  B
)

Proof of Theorem difeq2i
StepHypRef Expression
1 difeq1i.1 . 2  |-  A  =  B
2 difeq2 3110 . 2  |-  ( A  =  B  ->  ( C  \  A )  =  ( C  \  B
) )
31, 2ax-mp 7 1  |-  ( C 
\  A )  =  ( C  \  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1289    \ cdif 2994
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-ral 2364  df-rab 2368  df-dif 2999
This theorem is referenced by:  difeq12i  3114  inssddif  3238  difdif2ss  3254  dif32  3260  difabs  3261  symdif1  3262  notrab  3274  dif0  3350  difdifdirss  3363  dfif3  3402  difpr  3574  dif1o  6184  unfiin  6616
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