Theorem moeq 2914

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 2745	. . . 4 |- ( A e. _V <-> E. x x = A )
2		eueq 2910	. . . 4 |- ( A e. _V <-> E! x x = A )
3	1, 2	bitr3i 186	. . 3 |- ( E. x x = A <-> E! x x = A )
4	3	biimpi 120	. 2 |- ( E. x x = A -> E! x x = A )
5		df-mo 2030	. 2 |- ( E* x x = A <-> ( E. x x = A -> E! x x = A ) )
6	4, 5	mpbir 146	1 |- E* x x = A

Syntax hints:   -> wi 4   = wceq 1353   E.wex 1492   E!weu 2026   E*wmo 2027   e. wcel 2148   _Vcvv 2739

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030  df-clab 2164  df-cleq 2170  df-clel 2173  df-v 2741

This theorem is referenced by:  euxfr2dc  2924  reueq  2938  mosn  3630  sndisj  4001  disjxsn  4003  reusv1  4460  funopabeq  5254  funcnvsn  5263  fvmptg  5594  fvopab6  5614  ovmpt4g  5999  ovi3  6013  ov6g  6014  oprabex3  6132  1stconst  6224  2ndconst  6225  axaddf  7869  axmulf  7870