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Theorem difeq1i 3103
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 3100 . 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 1287    \ cdif 2985
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rab 2364  df-dif 2990
This theorem is referenced by:  difeq12i  3105  indif1  3233  indifcom  3234  difun1  3248  notab  3258  notrab  3265  difprsn1  3561  difprsn2  3562  orddif  4338  resdmdfsn  4724  phplem1  6522  dfn2  8622
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