Theorem wunun 9109

Description: A weak universe is closed under binary union. (Contributed by Mario Carneiro, 2-Jan-2017.)

Hypotheses

Ref	Expression
wununi.1
wununi.2
wunpr.3

Assertion

Ref	Expression
wunun

Proof of Theorem wunun

Step	Hyp	Ref	Expression
1		wununi.2	. . 3
2		wunpr.3	. . 3
3		uniprg 4263	. . 3
4	1, 2, 3	syl2anc 661	. 2
5		wununi.1	. . 3
6	5, 1, 2	wunpr 9108	. . 3
7	5, 6	wununi 9105	. 2
8	4, 7	eqeltrrd 2546	1

Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  u.cun 3473  {cpr 4031  U.cuni 4249  cwun 9099

This theorem is referenced by:  wuntp  9110  wunsuc  9116  wunfi  9120  wunxp  9123  wuntpos  9133  wunsets  14659  catcoppccl  15435

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-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-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-pr 4032  df-uni 4250  df-tr 4546  df-wun 9101