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Theorem iinrab2 4156
 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 4109 . . . . . 6
2 0iin 4151 . . . . . 6
31, 2syl6eq 2486 . . . . 5
43ineq1d 3543 . . . 4
5 incom 3535 . . . . 5
6 inv1 3656 . . . . 5
75, 6eqtri 2458 . . . 4
84, 7syl6eq 2486 . . 3
9 rzal 3731 . . . 4
10 rabid2 2887 . . . . 5
11 ralcom 2870 . . . . 5
1210, 11bitr2i 243 . . . 4
139, 12sylib 190 . . 3
148, 13eqtrd 2470 . 2
15 iinrab 4155 . . . 4
1615ineq1d 3543 . . 3
17 ssrab2 3430 . . . 4
18 dfss 3337 . . . 4
1917, 18mpbi 201 . . 3
2016, 19syl6eqr 2488 . 2
2114, 20pm2.61ine 2682 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   wne 2601  wral 2707  crab 2711  cvv 2958   cin 3321   wss 3322  c0 3630  ciin 4096 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rab 2716  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-nul 3631  df-iin 4098
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