Theorem iswun 9103

Description: Properties of a weak universe. (Contributed by Mario Carneiro, 2-Jan-2017.)

Assertion

Ref	Expression
iswun

Distinct variable group:   ,,

Proof of Theorem iswun

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		treq 4551	. . 3
2		neeq1 2738	. . 3
3		eleq2 2530	. . . . 5
4		eleq2 2530	. . . . 5
5		eleq2 2530	. . . . . 6
6	5	raleqbi1dv 3062	. . . . 5
7	3, 4, 6	3anbi123d 1299	. . . 4
8	7	raleqbi1dv 3062	. . 3
9	1, 2, 8	3anbi123d 1299	. 2
10		df-wun 9101	. 2
11	9, 10	elab2g 3248	1

Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  e.wcel 1818  =/=wne 2652  A.wral 2807  c0 3784  ~Pcpw 4012  {cpr 4031  U.cuni 4249  Trwtr 4545  cwun 9099

This theorem is referenced by:  wuntr  9104  wununi  9105  wunpw  9106  wunpr  9108  wun0  9117  intwun  9134  r1limwun  9135  wunex2  9137  tskwun  9183  gruwun  9212  pwinfi2  37747

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-an 371  df-3an 975  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-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-wun 9101