Theorem intiin 4384

Description: Class intersection in terms of indexed intersection. Definition in [Stoll] p. 44. (Contributed by NM, 28-Jun-1998.)

Assertion

Ref	Expression
intiin

Distinct variable group:   ,

Proof of Theorem intiin

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfint2 4288	. 2
2		df-iin 4333	. 2
3	1, 2	eqtr4i 2489	1

Syntax hints:  =wceq 1395  {cab 2442  A.wral 2807  |^|cint 4286  |^|_ciin 4331

This theorem is referenced by:  relint  5131  intpreima  6018  ixpint  7516  firest  14830  efger  16736  rintopn  19418  intcld  19541  iundifdifd  27429  iundifdif  27430

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-ral 2812  df-int 4287  df-iin 4333