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Theorem difeq2i 3059
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 3056 . 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 1243    \ cdif 2914
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ral 2311  df-rab 2315  df-dif 2920
This theorem is referenced by:  difeq12i  3060  inssddif  3178  difdif2ss  3194  dif32  3200  difabs  3201  symdif1  3202  notrab  3214  dif0  3294  difdifdirss  3307  dfif3  3343  dif1o  6021
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