Theorem eueq1 2851

Description: Equality has existential uniqueness. (Contributed by NM, 5-Apr-1995.)

Hypothesis

Ref	Expression
eueq1.1	|- A e. _V

Assertion

Ref	Expression
eueq1	|- E! x x = A

Distinct variable group:   x, A

Proof of Theorem eueq1

Step	Hyp	Ref	Expression
1		eueq1.1	. 2 |- A e. _V
2		eueq 2850	. 2 |- ( A e. _V <-> E! x x = A )
3	1, 2	mpbi 144	1 |- E! x x = A

Syntax hints:   = wceq 1331   e. wcel 1480   E!weu 1997   _Vcvv 2681

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 2119

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683

This theorem is referenced by:  eueq2dc  2852  eueq3dc  2853  fsn  5585