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Theorem funimaex 5187
Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep 4028. 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 5186 . 2  |-  ( ( Fun  A  /\  B  e.  _V )  ->  ( A " B )  e. 
_V )
31, 2mpan2 655 1  |-  ( Fun 
A  ->  ( A " B )  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 6    e. wcel 1621   _Vcvv 2727   "cima 4583   Fun wfun 4586
This theorem is referenced by:  isarep2  5189  isofr  5691  isose  5692  f1oweALT  5703  f1opw  5924  tz9.12lem2  7344  hsmexlem4  7939  hsmexlem5  7940  zorn2lem7  8013  uniimadom  8050  zexALT  9921  fbasrn  17411  fnwe2lem2  26314
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-rep 4028  ax-sep 4038  ax-nul 4046  ax-pr 4108
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-br 3921  df-opab 3975  df-id 4202  df-xp 4594  df-cnv 4596  df-co 4597  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601  df-fun 4602
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