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Theorem dfrn3 5051
 Description: Alternate definition of range. Definition 6.5(2) of [TakeutiZaring] p. 24. (Contributed by NM, 28-Dec-1996.)
Assertion
Ref Expression
dfrn3
Distinct variable group:   ,,

Proof of Theorem dfrn3
StepHypRef Expression
1 dfrn2 5050 . 2
2 df-br 4205 . . . 4
32exbii 1592 . . 3
43abbii 2547 . 2
51, 4eqtri 2455 1
 Colors of variables: wff set class Syntax hints:  wex 1550   wceq 1652   wcel 1725  cab 2421  cop 3809   class class class wbr 4204   crn 4870 This theorem is referenced by:  elrn2g  5052  elrn2  5100  csbrng  5105  imadmrn  5206  imassrn  5207  csbrngVD  28862 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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  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-br 4205  df-opab 4259  df-cnv 4877  df-dm 4879  df-rn 4880
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