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Theorem funimaex 5671
 Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep 4563. Axiom 39(vi) of [Quine] p. 284. Compare Exercise 9 of [TakeutiZaring] p. 29. (Contributed by NM, 17-Nov-2002.)
Hypothesis
Ref Expression
zfrep5.1
Assertion
Ref Expression
funimaex

Proof of Theorem funimaex
StepHypRef Expression
1 zfrep5.1 . 2
2 funimaexg 5670 . 2
31, 2mpan2 671 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  e.wcel 1818   cvv 3109  "cima 5007  Funwfun 5587 This theorem is referenced by:  isarep2  5673  isofr  6238  isose  6239  f1opw  6529  f1oweALT  6784  tz9.12lem2  8227  hsmexlem4  8830  hsmexlem5  8831  zorn2lem7  8903  uniimadom  8940  zexALT  10908  fbasrn  20385  fnwe2lem2  30997 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-rep 4563  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-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-id 4800  df-xp 5010  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-fun 5595
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