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Theorem riinrab 4158
 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 4156 . . 3
2 rzal 3721 . . . . 5
32ralrimivw 2782 . . . 4
4 rabid2 2877 . . . 4
53, 4sylibr 204 . . 3
61, 5eqtrd 2467 . 2
7 ssrab2 3420 . . . . 5
87rgenw 2765 . . . 4
9 riinn0 4157 . . . 4
108, 9mpan 652 . . 3
11 iinrab 4145 . . 3
1210, 11eqtrd 2467 . 2
136, 12pm2.61ine 2674 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wne 2598  wral 2697  crab 2701   cin 3311   wss 3312  c0 3620  ciin 4086 This theorem is referenced by:  acsfn1  13878  acsfn1c  13879  acsfn2  13880  cntziinsn  15125  csscld  19195  acsfn1p  27465 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621  df-iin 4088
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