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Theorem funimaex 5494
Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep 4284. 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 5493 . 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 2920   "cima 4844   Fun wfun 5411
This theorem is referenced by:  isarep2  5496  isofr  6025  isose  6026  f1oweALT  6037  f1opw  6262  tz9.12lem2  7674  hsmexlem4  8269  hsmexlem5  8270  zorn2lem7  8342  uniimadom  8379  zexALT  10260  fbasrn  17873  fnwe2lem2  27020
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 2389  ax-rep 4284  ax-sep 4294  ax-nul 4302  ax-pr 4367
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 2262  df-mo 2263  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-rab 2679  df-v 2922  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-br 4177  df-opab 4231  df-id 4462  df-xp 4847  df-cnv 4849  df-co 4850  df-dm 4851  df-rn 4852  df-res 4853  df-ima 4854  df-fun 5419
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