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Theorem dfse2 5375
Description: Alternate definition of set-like relation. (Contributed by Mario Carneiro, 23-Jun-2015.)
Assertion
Ref Expression
dfse2
Distinct variable groups:   ,   ,

Proof of Theorem dfse2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-se 4844 . 2
2 dfrab3 3772 . . . . 5
3 vex 3112 . . . . . . 7
4 iniseg 5373 . . . . . . 7
53, 4ax-mp 5 . . . . . 6
65ineq2i 3696 . . . . 5
72, 6eqtr4i 2489 . . . 4
87eleq1i 2534 . . 3
98ralbii 2888 . 2
101, 9bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  {cab 2442  A.wral 2807  {crab 2811   cvv 3109  i^icin 3474  {csn 4029   class class class wbr 4452  Sewse 4841  `'ccnv 5003  "cima 5007
This theorem is referenced by:  isoselem  6237  fnse  6917
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-se 4844  df-xp 5010  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017
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