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Theorem rintn0 4184
 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 3535 . 2
2 intssuni2 4077 . . . 4
3 ssid 3369 . . . . 5
4 sspwuni 4179 . . . . 5
53, 4mpbi 201 . . . 4
62, 5syl6ss 3362 . . 3
7 df-ss 3336 . . 3
86, 7sylib 190 . 2
91, 8syl5eq 2482 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wne 2601   cin 3321   wss 3322  c0 3630  cpw 3801  cuni 4017  cint 4052 This theorem is referenced by:  mrerintcl  13827  ismred2  13833 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-nul 3631  df-pw 3803  df-uni 4018  df-int 4053
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