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Theorem abrexss 23056
 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 2606 . . . 4
2 nfcv 2432 . . . . 5
3 abrexss.1 . . . . 5
42, 3nfel 2440 . . . 4
5 eleq1 2356 . . . 4
6 vex 2804 . . . . 5
76a1i 10 . . . 4
8 id 19 . . . . 5
98r19.21bi 2654 . . . 4
101, 4, 5, 7, 9elabreximd 23055 . . 3
1110ex 423 . 2
1211ssrdv 3198 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1632   wcel 1696  cab 2282  wnfc 2419  wral 2556  wrex 2557  cvv 2801   wss 3165 This theorem is referenced by:  funimass4f  23058  measvunilem  23555 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-v 2803  df-in 3172  df-ss 3179
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