Theorem pwuninel2 7022

Description: Direct proof of pwuninel 7023 avoiding functions and thus several ZF axioms. (Contributed by Stefan O'Rear, 22-Feb-2015.)

Assertion

Ref	Expression
pwuninel2

Proof of Theorem pwuninel2

Step	Hyp	Ref	Expression
1		pwnss 4617	. 2
2		elssuni 4279	. 2
3	1, 2	nsyl 121	1

Syntax hints:  -.wn 3  ->wi 4  e.wcel 1818  C_wss 3475  ~Pcpw 4012  U.cuni 4249

This theorem is referenced by:  pwuninel  7023

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  ax-sep 4573

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-nel 2655  df-rab 2816  df-v 3111  df-in 3482  df-ss 3489  df-pw 4014  df-uni 4250