Theorem moeq 2887

Description: There is at most one set equal to a class. (Contributed by NM, 8-Mar-1995.)

Assertion

Ref	Expression
moeq	|- E* x x = A

Distinct variable group:   x, A

Proof of Theorem moeq

Step	Hyp	Ref	Expression
1		isset 2718	. . . 4 |- ( A e. _V <-> E. x x = A )
2		eueq 2883	. . . 4 |- ( A e. _V <-> E! x x = A )
3	1, 2	bitr3i 185	. . 3 |- ( E. x x = A <-> E! x x = A )
4	3	biimpi 119	. 2 |- ( E. x x = A -> E! x x = A )
5		df-mo 2010	. 2 |- ( E* x x = A <-> ( E. x x = A -> E! x x = A ) )
6	4, 5	mpbir 145	1 |- E* x x = A

Syntax hints:   -> wi 4   = wceq 1335   E.wex 1472   E!weu 2006   E*wmo 2007   e. wcel 2128   _Vcvv 2712

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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010  df-clab 2144  df-cleq 2150  df-clel 2153  df-v 2714

This theorem is referenced by:  euxfr2dc  2897  reueq  2911  mosn  3595  sndisj  3961  disjxsn  3963  reusv1  4418  funopabeq  5206  funcnvsn  5215  fvmptg  5544  fvopab6  5564  ovmpt4g  5943  ovi3  5957  ov6g  5958  oprabex3  6077  1stconst  6168  2ndconst  6169  axaddf  7788  axmulf  7789