Theorem iineq2d 4351

Description: Equality deduction for indexed intersection. (Contributed by NM, 7-Dec-2011.)

Hypotheses

Ref	Expression
iineq2d.1
iineq2d.2

Assertion

Ref	Expression
iineq2d

Proof of Theorem iineq2d

Step	Hyp	Ref	Expression
1		iineq2d.1	. . 3
2		iineq2d.2	. . . 4
3	2	ex 434	. . 3
4	1, 3	ralrimi 2857	. 2
5		iineq2 4348	. 2
6	4, 5	syl 16	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  F/wnf 1616  e.wcel 1818  A.wral 2807  |^|_ciin 4331

This theorem is referenced by:  iineq2dv  4353  pmapglbx  35493

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-iin 4333