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Theorem refssex 26353
 Description: Every set in a refinement has a superset in the original cover. (Contributed by Jeff Hankins, 18-Jan-2010.)
Assertion
Ref Expression
refssex
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem refssex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 refrel 26350 . . . . 5
21brrelex2i 4912 . . . 4
3 eqid 2436 . . . . . 6
4 eqid 2436 . . . . . 6
53, 4isref 26351 . . . . 5
65simplbda 608 . . . 4
72, 6mpancom 651 . . 3
8 sseq1 3362 . . . . 5
98rexbidv 2719 . . . 4
109rspccv 3042 . . 3
117, 10syl 16 . 2
1211imp 419 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wral 2698  wrex 2699  cvv 2949   wss 3313  cuni 4008   class class class wbr 4205  cref 26332 This theorem is referenced by:  reftr  26361  refssfne  26366 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4323  ax-nul 4331  ax-pow 4370  ax-pr 4396  ax-un 4694 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2703  df-rex 2704  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-pw 3794  df-sn 3813  df-pr 3814  df-op 3816  df-uni 4009  df-br 4206  df-opab 4260  df-xp 4877  df-rel 4878  df-ref 26336
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