Theorem funimaex 3582

Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep 2698. Axiom 39(vi) of [Quine] p. 284. Compare Exercise 9 of [TakeutiZaring] p. 29.

Hypothesis

Ref	Expression
zfrep5.1	|- B e. V

Assertion

Ref	Expression
funimaex	|- (Fun A -> (A"B) e. V)

Proof of Theorem funimaex

Step	Hyp	Ref	Expression
1		zfrep5.1	. 2 |- B e. V
2		funimaexg 3581	. 2 |- ((Fun A /\ B e. V) -> (A"B) e. V)
3	1, 2	mpan2 698	1 |- (Fun A -> (A"B) e. V)

Syntax hints:   -> wi 3   e. wcel 960  Vcvv 1814  "cima 3179  Fun wfun 3182

This theorem is referenced by:  isarep2 3584  isofrlem 3907  f1oweALT 3912  tz7.44-3 3936  tz9.12lem2 4670  zorn2lem7 4804  uniimadom 4820

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-13 971  ax-14 972  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462  ax-rep 2698  ax-sep 2708  ax-pow 2748  ax-pr 2785

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385  df-clab 1467  df-cleq 1472  df-clel 1475  df-ne 1590  df-rex 1653  df-v 1815  df-dif 2052  df-un 2053  df-in 2054  df-ss 2056  df-nul 2284  df-pw 2406  df-sn 2416  df-pr 2417  df-op 2420  df-br 2625  df-opab 2672  df-id 2841  df-xp 3190  df-cnv 3192  df-co 3193  df-dm 3194  df-rn 3195  df-res 3196  df-ima 3197  df-fun 3198

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