Theorem funimaex 3568

Description: The image of a set under any function is also a set. Equivalent of Axiom of Replacement ax-rep 2688. 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 3567	. 2 |- ((Fun A /\ B e. V) -> (A"B) e. V)
3	1, 2	mpan2 695	1 |- (Fun A -> (A"B) e. V)

Syntax hints:   -> wi 3   e. wcel 956  Vcvv 1807  "cima 3168  Fun wfun 3171

This theorem is referenced by:  isarep2 3570  isofrlem 3892  f1oweALT 3897  tz7.44-3 3921  tz9.12lem2 4640  zorn2lem7 4774  uniimadom 4790

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-11 965  ax-12 966  ax-13 967  ax-14 968  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457  ax-rep 2688  ax-sep 2698  ax-pow 2737  ax-pr 2774

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-eu 1380  df-mo 1381  df-clab 1462  df-cleq 1467  df-clel 1470  df-ne 1584  df-rex 1647  df-v 1808  df-dif 2045  df-un 2046  df-in 2047  df-ss 2049  df-nul 2277  df-pw 2398  df-sn 2408  df-pr 2409  df-op 2412  df-br 2615  df-opab 2662  df-id 2830  df-xp 3179  df-cnv 3181  df-co 3182  df-dm 3183  df-rn 3184  df-res 3185  df-ima 3186  df-fun 3187

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