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Theorem seex 4548
 Description: The -preimage of an element of the base set in a set-like relation is a set. (Contributed by Mario Carneiro, 19-Nov-2014.)
Assertion
Ref Expression
seex Se
Distinct variable groups:   ,   ,   ,

Proof of Theorem seex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-se 4545 . 2 Se
2 breq2 4219 . . . . 5
32rabbidv 2950 . . . 4
43eleq1d 2504 . . 3
54rspccva 3053 . 2
61, 5sylanb 460 1 Se
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  wral 2707  crab 2711  cvv 2958   class class class wbr 4215   Se wse 4542 This theorem is referenced by:  wereu2  4582  fnse  6466  ordtypelem10  7499  setlikespec  25467 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-3an 939  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-ral 2712  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-br 4216  df-se 4545
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