Theorem iunss1 4342

Description: Subclass theorem for indexed union. (Contributed by NM, 10-Dec-2004.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)

Assertion

Ref	Expression
iunss1

Distinct variable groups:   ,   ,

Proof of Theorem iunss1

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ssrexv 3564	. . 3
2		eliun 4335	. . 3
3		eliun 4335	. . 3
4	1, 2, 3	3imtr4g 270	. 2
5	4	ssrdv 3509	1

Syntax hints:  ->wi 4  e.wcel 1818  E.wrex 2808  C_wss 3475  U_ciun 4330

This theorem is referenced by:  iuneq1  4344  iunxdif2  4378  oelim2  7263  fsumiun  13635  ovolfiniun  21912  uniioovol  21988  usgreghash2spotv  25066  volsupnfl  30059  bnj1413  34091  bnj1408  34092

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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-iun 4332