Theorem iunconst 4339

Description: Indexed union of a constant class, i.e. where does not depend on . (Contributed by NM, 5-Sep-2004.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)

Assertion

Ref	Expression
iunconst

Distinct variable groups:   ,   ,

Proof of Theorem iunconst

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		r19.9rzv 3923	. . 3
2		eliun 4335	. . 3
3	1, 2	syl6rbbr 264	. 2
4	3	eqrdv 2454	1

Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  =/=wne 2652  E.wrex 2808  c0 3784  U_ciun 4330

This theorem is referenced by:  iununi  4415  oe1m  7213  oarec  7230  oelim2  7263  mblfinlem2  30052  bnj1143  33849

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-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-nul 3785  df-iun 4332