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Theorem csbrng 4968
 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 3029 . . 3
2 sbcexg 2933 . . . . 5
3 sbcel2g 2992 . . . . . 6
43exbidv 1779 . . . . 5
52, 4bitrd 187 . . . 4
65abbidv 2233 . . 3
71, 6eqtrd 2148 . 2
8 dfrn3 4696 . . 3
98csbeq2i 2997 . 2
10 dfrn3 4696 . 2
117, 9, 103eqtr4g 2173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1314  wex 1451   wcel 1463  cab 2101  wsbc 2880  csb 2973  cop 3498   crn 4508 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-14 1475  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-sep 4014  ax-pow 4066  ax-pr 4099 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-sbc 2881  df-csb 2974  df-un 3043  df-in 3045  df-ss 3052  df-pw 3480  df-sn 3501  df-pr 3502  df-op 3504  df-br 3898  df-opab 3958  df-cnv 4515  df-dm 4517  df-rn 4518 This theorem is referenced by:  sbcfg  5239
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