Theorem prm 3791

Description: A pair containing a set is inhabited. (Contributed by Jim Kingdon, 21-Sep-2018.)

Hypothesis

Ref	Expression
prnz.1	|- A e. _V

Assertion

Ref	Expression
prm	|- E. x x e. { A , B }

Distinct variable groups:   x, A   x, B

Proof of Theorem prm

Step	Hyp	Ref	Expression
1		prnz.1	. 2 |- A e. _V
2		prmg 3789	. 2 |- ( A e. _V -> E. x x e. { A , B } )
3	1, 2	ax-mp 5	1 |- E. x x e. { A , B }

Syntax hints:   E.wex 1538   e. wcel 2200   _Vcvv 2799   {cpr 3667

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-un 3201  df-sn 3672  df-pr 3673

This theorem is referenced by: (None)