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Theorem args 4908
 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 2689 . . . . . 6
2 imasng 4904 . . . . . 6
31, 2ax-mp 5 . . . . 5
43eqeq1i 2147 . . . 4
54exbii 1584 . . 3
6 euabsn 3593 . . 3
75, 6bitr4i 186 . 2
87abbii 2255 1
 Colors of variables: wff set class Syntax hints:   wceq 1331  wex 1468   wcel 1480  weu 1999  cab 2125  cvv 2686  csn 3527   class class class wbr 3929  cima 4542 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-sbc 2910  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-xp 4545  df-cnv 4547  df-dm 4549  df-rn 4550  df-res 4551  df-ima 4552 This theorem is referenced by: (None)
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