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Theorem riinrab 4406
 Description: Relative intersection of a relative abstraction. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
riinrab
Distinct variable groups:   ,,   ,,

Proof of Theorem riinrab
StepHypRef Expression
1 riin0 4404 . . 3
2 rzal 3931 . . . . 5
32ralrimivw 2872 . . . 4
4 rabid2 3035 . . . 4
53, 4sylibr 212 . . 3
61, 5eqtrd 2498 . 2
7 ssrab2 3584 . . . . 5
87rgenw 2818 . . . 4
9 riinn0 4405 . . . 4
108, 9mpan 670 . . 3
11 iinrab 4392 . . 3
1210, 11eqtrd 2498 . 2
136, 12pm2.61ine 2770 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  =/=wne 2652  A.wral 2807  {crab 2811  i^icin 3474  C_wss 3475   c0 3784  |^|_ciin 4331 This theorem is referenced by:  acsfn1  15058  acsfn1c  15059  acsfn2  15060  cntziinsn  16372  csscld  21689  acsfn1p  31148 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-iin 4333
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