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Theorem csbnegg 7209
 Description: Move class substitution in and out of the negative of a number. (Contributed by NM, 1-Mar-2008.) (Proof shortened by Andrew Salmon, 22-Oct-2011.)
Assertion
Ref Expression
csbnegg

Proof of Theorem csbnegg
StepHypRef Expression
1 csbov2g 5546 . 2
2 df-neg 7185 . . 3
32csbeq2i 2876 . 2
4 df-neg 7185 . 2
51, 3, 43eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  csb 2852  (class class class)co 5512  cc0 6889   cmin 7182  cneg 7183 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  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-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-sbc 2765  df-csb 2853  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515  df-neg 7185 This theorem is referenced by: (None)
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