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Theorem args 4722
 Description: Two ways to express the class of unique-valued arguments of , which is the same as the domain of whenever is a function. The left-hand side of the equality is from Definition 10.2 of [Quine] p. 65. Quine uses the notation "arg " for this class (for which we have no separate notation). (Contributed by NM, 8-May-2005.)
Assertion
Ref Expression
args
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem args
StepHypRef Expression
1 vex 2577 . . . . . 6
2 imasng 4718 . . . . . 6
31, 2ax-mp 7 . . . . 5
43eqeq1i 2063 . . . 4
54exbii 1512 . . 3
6 euabsn 3468 . . 3
75, 6bitr4i 180 . 2
87abbii 2169 1
 Colors of variables: wff set class Syntax hints:   wceq 1259  wex 1397   wcel 1409  weu 1916  cab 2042  cvv 2574  csn 3403   class class class wbr 3792  cima 4376 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955  ax-pr 3972 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-sbc 2788  df-un 2950  df-in 2952  df-ss 2959  df-pw 3389  df-sn 3409  df-pr 3410  df-op 3412  df-br 3793  df-opab 3847  df-xp 4379  df-cnv 4381  df-dm 4383  df-rn 4384  df-res 4385  df-ima 4386 This theorem is referenced by: (None)
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