Theorem snm 3713

Description: The singleton of a set is inhabited. (Contributed by Jim Kingdon, 11-Aug-2018.)

Hypothesis

Ref	Expression
snnz.1	|- A e. _V

Assertion

Ref	Expression
snm	|- E. x x e. { A }

Distinct variable group:   x, A

Proof of Theorem snm

Step	Hyp	Ref	Expression
1		snnz.1	. 2 |- A e. _V
2		snmg 3711	. 2 |- ( A e. _V -> E. x x e. { A } )
3	1, 2	ax-mp 5	1 |- E. x x e. { A }

Syntax hints:   E.wex 1492   e. wcel 2148   _Vcvv 2738   {csn 3593

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-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2740  df-sn 3599

This theorem is referenced by:  mss  4227  ssfilem  6875  diffitest  6887  djuexb  7043  exmidonfinlem  7192  exmidfodomrlemim  7200  cc2lem  7265