Theorem iineq1 4345

Description: Equality theorem for indexed intersection. (Contributed by NM, 27-Jun-1998.)

Assertion

Ref	Expression
iineq1

Distinct variable groups:   ,   ,

Proof of Theorem iineq1

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		raleq 3054	. . 3
2	1	abbidv 2593	. 2
3		df-iin 4333	. 2
4		df-iin 4333	. 2
5	2, 3, 4	3eqtr4g 2523	1

Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  {cab 2442  A.wral 2807  |^|_ciin 4331

This theorem is referenced by:  iinrab2  4393  iinvdif  4402  riin0  4404  iin0  4626  xpriindi  5144  cmpfi  19908  ptbasfi  20082  fclsval  20509  taylfval  22754  polvalN  35629

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-iin 4333