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Theorem iinrab2 4332
 Description: Indexed intersection of a restricted class builder. (Contributed by NM, 6-Dec-2011.)
Assertion
Ref Expression
iinrab2
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem iinrab2
StepHypRef Expression
1 iineq1 4284 . . . . . 6
2 0iin 4327 . . . . . 6
31, 2syl6eq 2521 . . . . 5
43ineq1d 3624 . . . 4
5 incom 3616 . . . . 5
6 inv1 3764 . . . . 5
75, 6eqtri 2493 . . . 4
84, 7syl6eq 2521 . . 3
9 rzal 3862 . . . 4
10 rabid2 2954 . . . . 5
11 ralcom 2937 . . . . 5
1210, 11bitr2i 258 . . . 4
139, 12sylib 201 . . 3
148, 13eqtrd 2505 . 2
15 iinrab 4331 . . . 4
1615ineq1d 3624 . . 3
17 ssrab2 3500 . . . 4
18 dfss 3405 . . . 4
1917, 18mpbi 213 . . 3
2016, 19syl6eqr 2523 . 2
2114, 20pm2.61ine 2726 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452   wne 2641  wral 2756  crab 2760  cvv 3031   cin 3389   wss 3390  c0 3722  ciin 4270 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rab 2765  df-v 3033  df-dif 3393  df-in 3397  df-ss 3404  df-nul 3723  df-iin 4272 This theorem is referenced by: (None)
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