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Theorem iinrab2 4029
 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 3983 . . . . . 6
2 0iin 4024 . . . . . 6
31, 2syl6eq 2401 . . . . 5
43ineq1d 3456 . . . 4
5 incom 3448 . . . . 5
6 inv1 3577 . . . . 5
75, 6eqtri 2373 . . . 4
84, 7syl6eq 2401 . . 3
9 rzal 3651 . . . 4
10 rabid2 2788 . . . . 5
11 ralcom 2771 . . . . 5
1210, 11bitr2i 241 . . . 4
139, 12sylib 188 . . 3
148, 13eqtrd 2385 . 2
15 iinrab 4028 . . . 4
1615ineq1d 3456 . . 3
17 ssrab2 3351 . . . 4
18 dfss 3260 . . . 4
1917, 18mpbi 199 . . 3
2016, 19syl6eqr 2403 . 2
2114, 20pm2.61ine 2592 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   wne 2516  wral 2614  crab 2618  cvv 2859   cin 3208   wss 3257  c0 3550  ciin 3970 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551  df-iin 3972 This theorem is referenced by: (None)
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