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Theorem abrexss 23993
 Description: A necessary condition for an image set to be a subset. (Contributed by Thierry Arnoux, 6-Feb-2017.)
Hypothesis
Ref Expression
abrexss.1
Assertion
Ref Expression
abrexss
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)

Proof of Theorem abrexss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfra1 2756 . . . 4
2 abrexss.1 . . . . 5
32nfcri 2566 . . . 4
4 eleq1 2496 . . . 4
5 vex 2959 . . . . 5
65a1i 11 . . . 4
7 id 20 . . . . 5
87r19.21bi 2804 . . . 4
91, 3, 4, 6, 8elabreximd 23991 . . 3
109ex 424 . 2
1110ssrdv 3354 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2422  wnfc 2559  wral 2705  wrex 2706  cvv 2956   wss 3320 This theorem is referenced by:  funimass4f  24044  measvunilem  24566 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958  df-in 3327  df-ss 3334
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