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Theorem riinrab 4401
 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 4399 . . 3
2 rzal 3929 . . . . 5
32ralrimivw 2879 . . . 4
4 rabid2 3039 . . . 4
53, 4sylibr 212 . . 3
61, 5eqtrd 2508 . 2
7 ssrab2 3585 . . . . 5
87rgenw 2825 . . . 4
9 riinn0 4400 . . . 4
108, 9mpan 670 . . 3
11 iinrab 4387 . . 3
1210, 11eqtrd 2508 . 2
136, 12pm2.61ine 2780 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1379   wne 2662  wral 2814  crab 2818   cin 3475   wss 3476  c0 3785  ciin 4326 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-in 3483  df-ss 3490  df-nul 3786  df-iin 4328 This theorem is referenced by:  acsfn1  14912  acsfn1c  14913  acsfn2  14914  cntziinsn  16167  csscld  21424  acsfn1p  30753
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