Theorem moeq 2935

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 2766	. . . 4 |- ( A e. _V <-> E. x x = A )
2		eueq 2931	. . . 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 2046	. 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 1364   E.wex 1503   E!weu 2042   E*wmo 2043   e. wcel 2164   _Vcvv 2760

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-eu 2045  df-mo 2046  df-clab 2180  df-cleq 2186  df-clel 2189  df-v 2762

This theorem is referenced by:  euxfr2dc  2945  reueq  2959  mosn  3654  sndisj  4025  disjxsn  4027  reusv1  4489  funopabeq  5290  funcnvsn  5299  fvmptg  5633  fvopab6  5654  ovmpt4g  6041  ovi3  6055  ov6g  6056  oprabex3  6181  1stconst  6274  2ndconst  6275  axaddf  7928  axmulf  7929