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Theorem rnoprab 6158
 Description: The range of an operation class abstraction. (Contributed by NM, 30-Aug-2004.) (Revised by David Abernethy, 19-Apr-2013.)
Assertion
Ref Expression
rnoprab
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem rnoprab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfoprab2 6123 . . 3
21rneqi 5098 . 2
3 rnopab 5117 . 2
4 exrot3 1760 . . . 4
5 opex 4429 . . . . . . 7
65isseti 2964 . . . . . 6
7 19.41v 1925 . . . . . 6
86, 7mpbiran 886 . . . . 5
982exbii 1594 . . . 4
104, 9bitri 242 . . 3
1110abbii 2550 . 2
122, 3, 113eqtri 2462 1
 Colors of variables: wff set class Syntax hints:   wa 360  wex 1551   wceq 1653  cab 2424  cop 3819  copab 4267   crn 4881  coprab 6084 This theorem is referenced by:  rnoprab2  6159  ellines  26088 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-cnv 4888  df-dm 4890  df-rn 4891  df-oprab 6087
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