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Theorem difeq1i 3087
Description: Inference adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002.)
Hypothesis
Ref Expression
difeq1i.1  |-  A  =  B
Assertion
Ref Expression
difeq1i  |-  ( A 
\  C )  =  ( B  \  C
)

Proof of Theorem difeq1i
StepHypRef Expression
1 difeq1i.1 . 2  |-  A  =  B
2 difeq1 3084 . 2  |-  ( A  =  B  ->  ( A  \  C )  =  ( B  \  C
) )
31, 2ax-mp 7 1  |-  ( A 
\  C )  =  ( B  \  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1285    \ cdif 2971
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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rab 2358  df-dif 2976
This theorem is referenced by:  difeq12i  3089  indif1  3216  indifcom  3217  difun1  3231  notab  3241  notrab  3248  difprsn1  3533  difprsn2  3534  orddif  4298  resdmdfsn  4681  phplem1  6387  dfn2  8368
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