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Theorem csbrng 5114
 Description: Distribute proper substitution through the range of a class. (Contributed by Alan Sare, 10-Nov-2012.)
Assertion
Ref Expression
csbrng

Proof of Theorem csbrng
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 csbabg 3310 . . 3
2 sbcexg 3211 . . . . 5
3 sbcel2g 3272 . . . . . 6
43exbidv 1636 . . . . 5
52, 4bitrd 245 . . . 4
65abbidv 2550 . . 3
71, 6eqtrd 2468 . 2
8 dfrn3 5060 . . 3
98csbeq2i 3277 . 2
10 dfrn3 5060 . 2
117, 9, 103eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4  wex 1550   wceq 1652   wcel 1725  cab 2422  wsbc 3161  csb 3251  cop 3817   crn 4879 This theorem is referenced by:  csbima12gALT  5214  csbima12gALTVD  29009 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 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-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-cnv 4886  df-dm 4888  df-rn 4889
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