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Theorem rintn0 4371
 Description: Relative intersection of a nonempty set. (Contributed by Stefan O'Rear, 3-Apr-2015.) (Revised by Mario Carneiro, 5-Jun-2015.)
Assertion
Ref Expression
rintn0

Proof of Theorem rintn0
StepHypRef Expression
1 incom 3624 . 2
2 intssuni2 4259 . . . 4
3 ssid 3450 . . . . 5
4 sspwuni 4366 . . . . 5
53, 4mpbi 212 . . . 4
62, 5syl6ss 3443 . . 3
7 df-ss 3417 . . 3
86, 7sylib 200 . 2
91, 8syl5eq 2496 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   wceq 1443   wne 2621   cin 3402   wss 3403  c0 3730  cpw 3950  cuni 4197  cint 4233 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ne 2623  df-ral 2741  df-rex 2742  df-v 3046  df-dif 3406  df-in 3410  df-ss 3417  df-nul 3731  df-pw 3952  df-uni 4198  df-int 4234 This theorem is referenced by:  mrerintcl  15496  ismred2  15502
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