Theorem iineq2i 4350

Description: Equality inference for indexed intersection. (Contributed by NM, 22-Oct-2003.)

Hypothesis

Ref	Expression
iuneq2i.1

Assertion

Ref	Expression
iineq2i

Proof of Theorem iineq2i

Step	Hyp	Ref	Expression
1		iineq2 4348	. 2
2		iuneq2i.1	. 2
3	1, 2	mprg 2820	1

Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  |^|_ciin 4331

This theorem is referenced by:  iinrab  4392  iinin1  4401  imaiinfv  30625  diaintclN  36785  dibintclN  36894  dihintcl  37071

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