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Theorem dfdm3 4465
 Description: Alternate definition of domain. Definition 6.5(1) of [TakeutiZaring] p. 24. (Contributed by NM, 28-Dec-1996.)
Assertion
Ref Expression
dfdm3 dom A = {xyx, y A}
Distinct variable group:   x,y,A

Proof of Theorem dfdm3
StepHypRef Expression
1 df-dm 4298 . 2 dom A = {xy xAy}
2 df-br 3756 . . . 4 (xAy ↔ ⟨x, y A)
32exbii 1493 . . 3 (y xAyyx, y A)
43abbii 2150 . 2 {xy xAy} = {xyx, y A}
51, 4eqtri 2057 1 dom A = {xyx, y A}
 Colors of variables: wff set class Syntax hints:   = wceq 1242  ∃wex 1378   ∈ wcel 1390  {cab 2023  ⟨cop 3370   class class class wbr 3755  dom cdm 4288 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-br 3756  df-dm 4298 This theorem is referenced by:  csbdmg  4472
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