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Theorem dfdm3 5017
 Description: Alternate definition of domain. Definition 6.5(1) of [TakeutiZaring] p. 24. (Contributed by NM, 28-Dec-1996.)
Assertion
Ref Expression
dfdm3
Distinct variable group:   ,,

Proof of Theorem dfdm3
StepHypRef Expression
1 df-dm 4847 . 2
2 df-br 4173 . . . 4
32exbii 1589 . . 3
43abbii 2516 . 2
51, 4eqtri 2424 1
 Colors of variables: wff set class Syntax hints:  wex 1547   wceq 1649   wcel 1721  cab 2390  cop 3777   class class class wbr 4172   cdm 4837 This theorem is referenced by:  cnextf  18050  csbdmg  27849 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-br 4173  df-dm 4847
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