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Theorem difeq1i 3232
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 3229 . 2  |-  ( A  =  B  ->  ( A  \  C )  =  ( B  \  C
) )
31, 2ax-mp 5 1  |-  ( A 
\  C )  =  ( B  \  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1342    \ cdif 3109
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-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-rab 2451  df-dif 3114
This theorem is referenced by:  difeq12i  3234  indif1  3363  indifcom  3364  difun1  3378  notab  3388  notrab  3395  difprsn1  3707  difprsn2  3708  orddif  4519  resdifcom  4897  resdmdfsn  4922  phplem1  6810  dfn2  9119
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