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Theorem funimaex 3562
Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep 2683. Axiom 39(vi) of [Quine] p. 284. Compare Exercise 9 of [TakeutiZaring] p. 29.
Hypothesis
Ref Expression
zfrep5.1 |- B e. V
Assertion
Ref Expression
funimaex |- (Fun A -> (A"B) e. V)
Proof of Theorem funimaex
StepHypRef Expression
1 zfrep5.1 . 2 |- B e. V
2 funimaexg 3561 . 2 |- ((Fun A /\ B e. V) -> (A"B) e. V)
31, 2mpan2 694 1 |- (Fun A -> (A"B) e. V)
Colors of variables: wff set class
Syntax hints:   -> wi 3   e. wcel 955  Vcvv 1802  "cima 3163  Fun wfun 3166
This theorem is referenced by:  isarep2 3564  isofrlem 3886  f1oweALT 3891  tz7.44-3 3915  tz9.12lem2 4632  zorn2lem7 4766  uniimadom 4782
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-13 966  ax-14 967  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452  ax-rep 2683  ax-sep 2693  ax-pow 2732  ax-pr 2769
This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376  df-clab 1457  df-cleq 1462  df-clel 1465  df-ne 1579  df-rex 1642  df-v 1803  df-dif 2039  df-un 2040  df-in 2041  df-ss 2043  df-nul 2271  df-pw 2392  df-sn 2402  df-pr 2403  df-op 2406  df-br 2610  df-opab 2657  df-id 2824  df-xp 3174  df-cnv 3176  df-co 3177  df-dm 3178  df-rn 3179  df-res 3180  df-ima 3181  df-fun 3182
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