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Theorem exse2 5240
 Description: Any set relation is set-like. (Contributed by Mario Carneiro, 22-Jun-2015.)
Assertion
Ref Expression
exse2 Se

Proof of Theorem exse2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-rab 2716 . . . . 5
2 vex 2961 . . . . . . . 8
3 vex 2961 . . . . . . . 8
42, 3breldm 5076 . . . . . . 7
54adantl 454 . . . . . 6
65abssi 3420 . . . . 5
71, 6eqsstri 3380 . . . 4
8 dmexg 5132 . . . 4
9 ssexg 4351 . . . 4
107, 8, 9sylancr 646 . . 3
1110ralrimivw 2792 . 2
12 df-se 4544 . 2 Se
1311, 12sylibr 205 1 Se
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wcel 1726  cab 2424  wral 2707  crab 2711  cvv 2958   wss 3322   class class class wbr 4214   Se wse 4541   cdm 4880 This theorem is referenced by:  dfac8clem  7915 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405  ax-un 4703 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-se 4544  df-cnv 4888  df-dm 4890  df-rn 4891
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