Theorem prm 3727

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 3725	. 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 1502   e. wcel 2158   _Vcvv 2749   {cpr 3605

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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-un 3145  df-sn 3610  df-pr 3611

This theorem is referenced by: (None)