Theorem prnz 4149

Description: A pair containing a set is not empty. (Contributed by NM, 9-Apr-1994.)

Hypothesis

Ref	Expression
prnz.1

Assertion

Ref	Expression
prnz

Proof of Theorem prnz

Step	Hyp	Ref	Expression
1		prnz.1	. . 3
2	1	prid1 4138	. 2
3	2	ne0ii 3791	1

Syntax hints:  e.wcel 1818  =/=wne 2652  cvv 3109  c0 3784  {cpr 4031

This theorem is referenced by:  prnzg  4150  opnz  4723  fiint  7817  wilthlem2  23343  edgwlk  24531  umgrabi  24983  shincli  26280  chincli  26378

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-nul 3785  df-sn 4030  df-pr 4032