Theorem moeq 2859

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 2692	. . . 4 |- ( A e. _V <-> E. x x = A )
2		eueq 2855	. . . 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 2003	. 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 1331   E.wex 1468   e. wcel 1480   E!weu 1999   E*wmo 2000   _Vcvv 2686

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-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688

This theorem is referenced by:  euxfr2dc  2869  reueq  2883  mosn  3560  sndisj  3925  disjxsn  3927  reusv1  4379  funopabeq  5159  funcnvsn  5168  fvmptg  5497  fvopab6  5517  ovmpt4g  5893  ovi3  5907  ov6g  5908  oprabex3  6027  1stconst  6118  2ndconst  6119  axaddf  7676  axmulf  7677