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Theorem csbnegg 9295
 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 6107 . 2
2 df-neg 9286 . . 3
32csbeq2i 3269 . 2
4 df-neg 9286 . 2
51, 3, 43eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  csb 3243  (class class class)co 6073  cc0 8982   cmin 9283  cneg 9284 This theorem is referenced by:  dvfsum2  19910 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076  df-neg 9286
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