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Theorem moeq 2710
Description: There is at most one set equal to a class. (Contributed by NM, 8-Mar-1995.)
Assertion
Ref Expression
moeq ∃*x x = A
Distinct variable group:   x,A

Proof of Theorem moeq
StepHypRef Expression
1 isset 2555 . . . 4 (A V ↔ x x = A)
2 eueq 2706 . . . 4 (A V ↔ ∃!x x = A)
31, 2bitr3i 175 . . 3 (x x = A∃!x x = A)
43biimpi 113 . 2 (x x = A∃!x x = A)
5 df-mo 1901 . 2 (∃*x x = A ↔ (x x = A∃!x x = A))
64, 5mpbir 134 1 ∃*x x = A
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  wex 1378   wcel 1390  ∃!weu 1897  ∃*wmo 1898  Vcvv 2551
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  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-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by:  euxfr2dc  2720  reueq  2732  mosn  3398  sndisj  3751  disjxsn  3753  reusv1  4156  funopabeq  4879  funcnvsn  4888  fvmptg  5191  fvopab6  5207  ovmpt4g  5565  ovi3  5579  ov6g  5580  oprabex3  5698  1stconst  5784  2ndconst  5785
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