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Theorem riinrab 4041
 Description: Relative intersection of a relative abstraction. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
riinrab
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem riinrab
StepHypRef Expression
1 riin0 4039 . . 3
2 rzal 3651 . . . . 5
32ralrimivw 2698 . . . 4
4 rabid2 2788 . . . 4
53, 4sylibr 203 . . 3
61, 5eqtrd 2385 . 2
7 ssrab2 3351 . . . . 5
87rgenw 2681 . . . 4
9 riinn0 4040 . . . 4
108, 9mpan 651 . . 3
11 iinrab 4028 . . 3
1210, 11eqtrd 2385 . 2
136, 12pm2.61ine 2592 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   wne 2516  wral 2614  crab 2618   cin 3208   wss 3257  c0 3550  ciin 3970 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-rex 2620  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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