Theorem ineqri 3691

Description: Inference from membership to intersection. (Contributed by NM, 21-Jun-1993.)

Hypothesis

Ref	Expression
ineqri.1

Assertion

Ref	Expression
ineqri

Distinct variable groups:   ,   ,   ,

Proof of Theorem ineqri

Step	Hyp	Ref	Expression
1		elin 3686	. . 3
2		ineqri.1	. . 3
3	1, 2	bitri 249	. 2
4	3	eqriv 2453	1

Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  i^icin 3474

This theorem is referenced by:  inidm  3706  inass  3707  dfin2  3733  indi  3743  inab  3765  in0  3811  pwin  4789  dmres  5299  dfres3  29188  inixp  30219

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-v 3111  df-in 3482