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Theorem funimaex 5517
Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep 4307. 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 5516 . 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 1725   _Vcvv 2943   "cima 4867   Fun wfun 5434
This theorem is referenced by:  isarep2  5519  isofr  6048  isose  6049  f1oweALT  6060  f1opw  6285  tz9.12lem2  7698  hsmexlem4  8293  hsmexlem5  8294  zorn2lem7  8366  uniimadom  8403  zexALT  10284  fbasrn  17899  fnwe2lem2  27058
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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2411  ax-rep 4307  ax-sep 4317  ax-nul 4325  ax-pr 4390
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2417  df-cleq 2423  df-clel 2426  df-nfc 2555  df-ne 2595  df-ral 2697  df-rex 2698  df-rab 2701  df-v 2945  df-dif 3310  df-un 3312  df-in 3314  df-ss 3321  df-nul 3616  df-if 3727  df-sn 3807  df-pr 3808  df-op 3810  df-br 4200  df-opab 4254  df-id 4485  df-xp 4870  df-cnv 4872  df-co 4873  df-dm 4874  df-rn 4875  df-res 4876  df-ima 4877  df-fun 5442
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