Theorem inab 3765

Description: Intersection of two class abstractions. (Contributed by NM, 29-Sep-2002.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

Assertion

Ref	Expression
inab

Proof of Theorem inab

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		sban 2140	. . 3
2		df-clab 2443	. . 3
3		df-clab 2443	. . . 4
4		df-clab 2443	. . . 4
5	3, 4	anbi12i 697	. . 3
6	1, 2, 5	3bitr4ri 278	. 2
7	6	ineqri 3691	1

Syntax hints:  /\wa 369  =wceq 1395  [wsb 1739  e.wcel 1818  {cab 2442  i^icin 3474

This theorem is referenced by:  inrab  3769  inrab2  3770  dfrab3  3772  orduniss2  6668  ssenen  7711  hashf1lem2  12505  ballotlem2  28427  dfiota3  29573  ptrest  30048  diophin  30706  bj-inrab  34495

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-or 370  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