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Theorem dfse2 5237
 Description: Alternate definition of set-like relation. (Contributed by Mario Carneiro, 23-Jun-2015.)
Assertion
Ref Expression
dfse2 Se
Distinct variable groups:   ,   ,

Proof of Theorem dfse2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-se 4542 . 2 Se
2 dfrab3 3617 . . . . 5
3 vex 2959 . . . . . . 7
4 iniseg 5235 . . . . . . 7
53, 4ax-mp 8 . . . . . 6
65ineq2i 3539 . . . . 5
72, 6eqtr4i 2459 . . . 4
87eleq1i 2499 . . 3
98ralbii 2729 . 2
101, 9bitri 241 1 Se
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652   wcel 1725  cab 2422  wral 2705  crab 2709  cvv 2956   cin 3319  csn 3814   class class class wbr 4212   Se wse 4539  ccnv 4877  cima 4881 This theorem is referenced by:  isoselem  6061  fnse  6463 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 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 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-se 4542  df-xp 4884  df-cnv 4886  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891
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