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Theorem funimaex 5601
Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep 4504. 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 5600 . 2  |-  ( ( Fun  A  /\  B  e.  _V )  ->  ( A " B )  e. 
_V )
31, 2mpan2 669 1  |-  ( Fun 
A  ->  ( A " B )  e.  _V )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1840   _Vcvv 3056   "cima 4943   Fun wfun 5517
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-9 1844  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378  ax-rep 4504  ax-sep 4514  ax-nul 4522  ax-pr 4627
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 974  df-tru 1406  df-ex 1632  df-nf 1636  df-sb 1762  df-eu 2240  df-mo 2241  df-clab 2386  df-cleq 2392  df-clel 2395  df-nfc 2550  df-ne 2598  df-ral 2756  df-rex 2757  df-rab 2760  df-v 3058  df-dif 3414  df-un 3416  df-in 3418  df-ss 3425  df-nul 3736  df-if 3883  df-sn 3970  df-pr 3972  df-op 3976  df-br 4393  df-opab 4451  df-id 4735  df-xp 4946  df-cnv 4948  df-co 4949  df-dm 4950  df-rn 4951  df-res 4952  df-ima 4953  df-fun 5525
This theorem is referenced by:  isarep2  5603  isofr  6175  isose  6176  f1opw  6464  f1oweALT  6720  tz9.12lem2  8156  hsmexlem4  8759  hsmexlem5  8760  zorn2lem7  8832  uniimadom  8869  zexALT  10842  fbasrn  20567  fnwe2lem2  35323
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