Theorem fin 5770

Description: Mapping into an intersection. (Contributed by NM, 14-Sep-1999.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)

Assertion

Ref	Expression
fin

Proof of Theorem fin

Step	Hyp	Ref	Expression
1		ssin 3719	. . . 4
2	1	anbi2i 694	. . 3
3		anandi 828	. . 3
4	2, 3	bitr3i 251	. 2
5		df-f 5597	. 2
6		df-f 5597	. . 3
7		df-f 5597	. . 3
8	6, 7	anbi12i 697	. 2
9	4, 5, 8	3bitr4i 277	1

Syntax hints:  <->wb 184  /\wa 369  i^icin 3474  C_wss 3475  rancrn 5005  Fnwfn 5588  -->wf 5589

This theorem is referenced by:  maprnin  27554

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  df-ss 3489  df-f 5597