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Theorem funimaex 5490
Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep 4280. 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  |-  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 5489 . 2  |-  ( ( Fun  A  /\  B  e.  _V )  ->  ( A " B )  e. 
_V )
31, 2mpan2 653 1  |-  ( Fun 
A  ->  ( A " B )  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1721   _Vcvv 2916   "cima 4840   Fun wfun 5407
This theorem is referenced by:  isarep2  5492  isofr  6021  isose  6022  f1oweALT  6033  f1opw  6258  tz9.12lem2  7670  hsmexlem4  8265  hsmexlem5  8266  zorn2lem7  8338  uniimadom  8375  zexALT  10256  fbasrn  17869  fnwe2lem2  27016
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-rep 4280  ax-sep 4290  ax-nul 4298  ax-pr 4363
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-br 4173  df-opab 4227  df-id 4458  df-xp 4843  df-cnv 4845  df-co 4846  df-dm 4847  df-rn 4848  df-res 4849  df-ima 4850  df-fun 5415
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